Developing analytical skills in GIS [304823]

Level 2
Developing analytical skills in GIS

Introduction

Over the last few years a [anonimizat]. [anonimizat], regional and national security authorities turned to new decision support tools such as Geographic Information Systems (GIS) and other information technologies to help them in finding better solutions. [anonimizat], analyse and correlate them.

Statistics are an important tool in crime analysis and police forces are using it in a [anonimizat]. Statistics help strategic decisions and turn vast amounts of meaningless numbers into a general picture (geographically and temporally identified) of crime events. Geostatistics are also crucial when working with spatial data. [anonimizat], the true value of information can be extract. By assuming that every crime point has a geographical location (in space) and that every point has a [anonimizat] (point) with all the others to construct a complete analysis scenario.

[anonimizat]-Led Policing (ILP) methods. [anonimizat]. This research combines statistical methods (cluster analysis) and spatial models with GIS based on police crime reports. It also details a [anonimizat] (enough) to enable accurate predictive models as well as to produce rigorous thematic maps. It is also an approach to “Intelligence-led policing” as a strategic methodology to provide tools for decision support by police departments.

[anonimizat], [anonimizat], the study and modelling of crime data to identify patterns have emerged as a new research field.

Content of training

Pattern & Standard Deviation

Standard Deviation

Definition

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the Greek small letter sigma).

It is a data classification method that finds the mean value of the observations then places class breaks above and below the mean at intervals of either 1, 2 or 3 [anonimizat]. This classification method shows how much the feature's attribute value varies from the mean. Using a diverging colour scheme to illustrate these values is useful to emphasize which observations are above the mean and which observations are below the mean.

Standard deviation: A [anonimizat], divided by the number of elements minus one. The standard deviation for a distribution is the square root of the variance.

Calculate standard deviation

A [anonimizat] “the confidence interval”.

The accepted level of normal values, calculated according to previous data.

Automated methods used to calculate the standard deviation:

Using ArcMap (Layer properties/ Symbology/ Classify/ Standard deviation)

Using Excel (insert function – Fx/ Statistical/ STDEV.P or STDEV.S)

Using a standard deviation calculator (you can easily find one on the internet)

The formula used to calculate standard deviation:

1. Find the Mean (the simple average of the numbers)

Mean = X1+X2+X3+ … +Xn / n

2. Find the Variance:

For each number: subtract the Mean and square the result (the squared difference).

Variance= the average of the squared differences.

Variance = ( (X1-mean)2 + (X2-mean)2 + (X3-mean)2 + … + (Xn-mean)2 ) / n

3. Standard deviation = square root of Variance

Standard deviation = √Variance

4. Calculate the first standard deviation interval

The minimum value of interval: mean – standard deviation

The maximum value of interval: mean + standard deviation

Statistics, classification and representation using St. Dev.

In a normal tendency:

– 68.2% of the values lie within 1st standard deviation of the mean

– 27.2% of the values lie between 1st and 2nd standard deviation

– 4.2% of the values lie between 2nd and 3rd standard deviation

– 0.4% of the values lie outside the 3rd standard deviation

For example, if you want to represent on a map the number of offenses by counties and reveal for each county if the values are in the normal range of 1st SD (blue colour), or are higher – between 1st and 2nd SD (yellow colour), between 2nd and 3rd (red colour).

Figure 2 – Number of offenses by county, represented thematically using standard deviation as classification method.

What it’s good for:

Seeing which features are above or below an average value.

Displaying data that has many values around the mean, and few further from the mean.

Smaller standard deviations reflect more clustered data. More clustered data means less extreme values. A data set with less extreme values has a more reliable mean. The standard deviation is therefore a good measure of the reliability of the mean value.

Disadvantages:

The map doesn’t show the actual values of the features, only how far their value is from the mean.

Very high or low values can skew the mean so that most features will fall in the same class. This classification method, should only be used for data-sets that show an approximately "standardized normal distribution" ("Gaussian distribution"). This constraint is the major disadvantage of this method.

Spatial Pattern Analysis

1.3.1 Introduction and environmental criminology

Spatial pattern analysis is the study of the spatial arrangements of points, lines or polygons in space. In police work, spatial pattern analysis is usually done by analysing points that represent events, points of interest or different types of offenses/ crimes. Point pattern analysis is the evaluation of the pattern, or distribution of a set of points on a surface. It is one of the most fundamental concepts in geography and spatial analysis.

Since G.I.S. can store geographic attributes and integrate spatial and other data for analytic purposes, it could assist in the reduction of linkage blindness and help identify crime series. Geographically coded information from police records can be used to detect crime trends and patterns, confirm the presence of persons within geographic areas and identify areas for patrol unit concentration.

Nowadays, Police is using new ways to fight crime: data sources about crimes and conditions including, time of day, location, number of victims, and many other variables to predict when and where crimes are likely to occur. A criminal’s actions can be modelled, as their actions reveal certain patterns, many of which are spatially related.

These spatial patterns can be used to predict events, as support for smart policing where officers can be deployed to certain locations to prevent criminal activity and to be able to respond more rapidly.

A range of methods can be applied to point pattern analysis, ranging from the simple to the complex. There are many similarities between the statistics used for point pattern analysis and those used in number analysis, although point pattern analysis also includes some special techniques.

In its most basic form, we can think of point pattern analysis as an attempt to analyse the occurrence of points in a particular space.

Often the first question asked is simply, how many points are there?

For example, how many robberies are there in a neighbourhood of a city?

How does that compare to a differing neighbourhood, or that city as a whole?

This is called studying the point’s frequency, intensity, or abundance.

To answer this and some other basic questions we can use the simple descriptive statistics that we would use for a numerical dataset: Count, Mean, Median, and Standard Deviation. Applying these, we can describe how dense a pattern is, where the centre of a set of points is, and how dispersed these points are.

According to Darcy Kim Rossmo, environmental criminologists set out to use the geographic imagination in concert with the sociological imagination to describe, understand and control criminal events. The crime setting or place, the where and when of the criminal act, makes up the fourth dimension of crime, the primary concern of environmental criminology.

As chaotic as crime may appear to be, there is often a rationality influencing the geography of its occurrence and some semblance of structure underlying its spatial distribution.

Offenders attack where they are comfortable and in surrounding which are known to them and where they may be confident of effecting escape. The victim is then selected by the circumstances in which she becomes available to the attacker and vulnerable to attack.

The Brantingham and Brantingham model of crime site selection: Crimes are most likely to occur in those areas where the awareness space of the offender intersects with perceived suitable targets. These ideas suggest that most offenders do not choose their crime sites randomly. While any given victim may be selected by chance, the process of such random selection is spatially structured whether the offender realizes it or not.

Targets are selected from an offender’s awareness space and assessed against the criteria of suitability (gain or profit) and risk (probability of being observed or apprehended), where suitable targets overlap the offender’s awareness space. A person’s awareness space forms part of his or her mental map and is built primarily, but not exclusively from the spatial experiences of the individual.

Where we go depends upon what we know – What we know depends on where we go.

A mental map is a representation of the spatial environment which an individual carry in his mind. Mental maps provide the outer limits of potential action space. It includes all present and past residences, schools, workplaces, social activity locations, possible travel routes and sites known to but never visited by the offender.

There is usually a buffer zone, however, centered on the criminal’s residence comparable to what Newton and Swoope (1987) term the coal-sack effect. Within this zone, targets are viewed as less desirable because of the perceived level of risk associated with operating too close to home.

Crime locations: There may be several locations involved in a case of serial murder, each with a slightly different geographic meaning:

Victim encounter locations

Points of first attack

Murder scenes

Body dump sites

Vehicle or property drop sites

1.3.2. Descriptive Statistics: centrography and usage of standard deviation in G.I.S.

Many of the standard descriptive statistics can be applied or slightly modified to describe spatial data. The focus of a point pattern analysis is firstly to examine the spatial distribution of the events, and secondly making inferences about the process that generated the point pattern.

Thus the first step in every point pattern analysis, as in every statistical and geostatistical analysis, is describe the dataset in hands with some descriptive indexes. In statistics we normally use mean and standard deviation to achieve this however here we are working in 2D space, so things are slightly more complicated.

Mean Centre

Is the mean of the X and Y coordinates for your set of points, giving the middle of the point pattern, the geographic centre (or the centre of concentration) for a set of features.

The mean centre is the average X and Y coordinate of all the features in the study area. It's useful for tracking changes in the distribution or for comparing the distributions of different types of features.

The mean centre is also known as “spatial mean” – the geographic centre of gravity, which reveals the central tendency of a point pattern. It provides a single summary location for a series of points and has a variety of geostatistical uses, which are sometimes classified together as centrography.

Central feature

Is a slightly different way to calculate middle and is the point in a pattern which minimizes the distance between itself and all other points. The Central Feature tool identifies the most centrally located feature in a point, line, or polygon input feature class. Distances from each feature centroid to every other feature centroid in the dataset are calculated and summed. Then the feature associated with the shortest accumulative distance to all other features (weighted if a weight is specified) is selected and copied to a newly created output feature class.

Standard Distance Deviation

Standard distance deviation is the standard deviation of the distance of each point from the mean centre. The standard distance measures the degree to which features are concentrated or dispersed around the geometric mean centre. The standard distance is a useful statistic as it provides a single summary measure of feature distribution around their centre.

The mean centre (spatial mean) serve as the basis for calculating the standard distance of a point pattern. Such measures can help describe two-dimensional distributions and allow comparisons between different sets of points.

Usually, the correlation between the offender’s home/ residence and his activity is relevant. “Like a person going shopping, a criminal will also go to locations that are convenient.”. (Canter, 1994)

Changes over time in the location of the spatial mean also allow for the calculation of the geographic equivalents of the concepts of velocity (rate of spatial change), acceleration (rate of change in velocity) and momentum (velocity multiplied by the number of points). (Rossmo, 1995)

Standard Deviational Ellipse

The problem with the standard distance is that it averages the standard deviation of the distances for both coordinates, so it does not take into account possible differences between the two dimensions. We can take those into account by plotting an ellipse, instead of a circle, with the two axis equal to the standard deviations of longitude and latitude.

A common way of measuring the trend for a set of points or areas is to calculate the standard distance separately in the x and y directions. These two measures define the axes of an ellipse encompassing the distribution of features. The ellipse allows you to see if the distribution of features is elongated and hence has a particular orientation.

While you can get a sense of the orientation by drawing the features on a map, calculating the standard deviational ellipse makes the trend clear.

Difference between standard distance deviation and standard deviational ellipse

The problem with the standard distance is that it averages the standard deviation of the distances for both coordinates, so it does not take into account possible differences between the two dimensions. We can take those into account by plotting an ellipse, instead of a circle, with the two axis equal to the standard deviations of longitude and latitude.

While the standard distance deviation is a good single measure of the dispersion of the incidents around the mean centre, it does not show the potential skewed nature of the data (anisotropy). The standard deviation ellipse gives dispersion in two dimensions.

Figure 7 – Differences between Standard Distance and Standard Deviational Ellipse

Using weights when measuring the distribution of features

Weight: a number that indicates the importance of a variable for a particular calculation. The larger the weight assigned to the variable, the more that variable will influence the outcome of the operation.

If you want to measure characteristics of locations, run your analysis without a Weight Field.

When some features are more important than others, you can use the Weight Field to represent those features differently. In this case, performing an unweighted analysis that only looks at fixed feature locations, may not be very meaningful.

Measuring the spatial characteristics of features when they are weighted by an attribute, can be very useful. For example, you might use the location of burglaries and the value of stolen items as weight, to calculate the center of interest.

Figure 8 – Points represented by weight (offences represented by importance)

Figure 9 – Standard distance with weight: Calculates standard distance for a set of offences, based on their importance.

Frequency and Density

Frequency in statistics

Crucial information we need when we deal with point patterns is a quantitative definition of the spatial distribution, for example how many events we have in a predefined window.

Frequency is the most basic way of evaluating a spatial pattern and is simply counting the number of points in your study area. To get density, you divide this total by unit of area or time in whatever units you deem are most appropriate: offenses per square mile, violent crimes per month, etc. Frequency and density should almost always be determined at the start of your analysis.

For example, given a point layer of offenses, containing the type of offense (theft/shoplifting/rape/ …) and time (day/night), a frequency operation would provide a count of how many offenses of each type happened during day and night.

The output table contains a new column: “FREQUENCY”, that counts the number of offenses grouped by the selected fields: type and time. Now we have a count of how many offenses of each type happened in which part of day.

Determine Frequency and Density for spatial data

Frequency may be constant across the study window, in that case in every square meter we would find the same number of points, and the process would be uniform. Most often the frequency is not constant and varies spatially throughout the study window, in that case the process is inhomogeneous.

For inhomogeneous processes, we need a way to determine the amount of spatial variation of the frequency.

Determine frequency and density for spatial data, using spatial join.

There are two ways of dealing with this problem:

Use a spatial division to count the number of events. (Count how many events are located in each sector’s geometry)

Quadrat counting, where the area is divided into rectangles and the number of events in each of them is counted. (Divide the window in square kilometres and count the number of events for each quadrant).

Count the number of events in a spatial division

Spatial join can be used to find out how many points fall inside a polygon. Using a set of administrative divisions, you can join data from another layer containing points, based on spatial location.

Using this technique (counting how many points are located in each sector’s geometric shape) you can find out, for example, how many offenses happened in each administrative division.

A new table is created, which contains the count of burglaries in each sector.

Quadrat Analysis

In quadrat analysis you divide your study area into subsections of equal size, and then calculate the frequency of points in each subsection. See the figure below for an example of this method:

The subsections used are normally square. This method provides a study-specific, numerical measure of frequency. The different values for each cell also give a mean value of frequency of points across the study area, as well as the ability to calculate variance between subsections.

Quadrat analysis is a simple, customizable, and valuable analysis tool. However, there are some criticisms of the method. Primarily, these arise from the ability to vary the size of the quadrat regions for each study. Therefore, quadrat analysis can provide different results for the same dataset using different sizes. Also, the result of quadrat analysis is a single measure of frequency for the entire study, so variations within the regions are disguised. This method must be applied in an appropriate manner for each study and an understanding of the dataset is needed before performing this technique.

We are interested in finding a pattern for a set of burglaries in Bucharest that are characterized by the same modus operandi.

To see how this tool works, you must fallow these steps:

Represent offenses on the map, using points;

Generate polygons for each square kilometre (fishnet);

Using a spatial join, count the number of offenses in each square kilometre;

Symbolize the square kilometres’ polygons with graduated colours, by the number of burglaries.

Dispersion & Arrangement:

Definition

Another set of questions in point pattern analysis concerns the relative pattern or arrangement of the points. Point patterns can be categorized as random, uniform, clustered or dispersed along the following two continuums:

• Random vs. Uniform (stratified, regular)

• Clustered vs. Dispersed

These two continuums are not necessarily related, and therefore a pattern of points could be randomly distributed in a clustered way (far right image), or stratified and dispersed (middle image). The attributes of one continuum have no effect on the attributes of the other continuum.

The difference between these types of distributions can be easily seen in our example, but there are techniques to quantify the amount of stratification or clustering. This allows one to determine exactly how clustered something is, or to compare two sets of points. One can see applications to crime analysis, for example being able to determine that the incidence of a certain type of crime is randomly distributed across a city or that it is clustered around a particular point of interest.

Complete Spatial Randomness: There are a number of techniques specifically designed for pattern analysis of point data. A concept that is common in these techniques is complete spatial randomness (CSR). CSR is a random or Poisson distribution of points in an area, the spatial version of a random or Poisson distribution of values in a numerical data set. Actual data is often contrasted with CSR and serves as a baseline for analysis.

Analyse patterns – Nearest Neighbour Index

One way in which patterns can be measured objectively is by nearest neighbour analysis. It can be used to identify a tendency towards clustering or dispersion. Nearest neighbour analysis gives an index that enables one region to be compared with another.

In real life it is often difficult to spot patterns in GIS. Nearest neighbour analysis provides a basic test to identify whether there are spatial patterns in the data and what the nature of these patterns might be. Unlike quadrat analysis, it uses distances between points as its basis.

While the spatial mean provides a way to measure central tendency in a point pattern, nearest neighbour analysis supplies a way to quantify spacing between points. Distance between points and their closest neighbours provide important information concerning a pattern’s degree of randomness. The ratio between the actual average nearest neighbour distance and the expected under an assumption of randomness provides a simple index for measuring divergence from randomness.

The Nearest Neighbour Index is a complicated tool to measure precisely the spatial distribution of a patter and see if it is regularly dispersed, randomly dispersed, or clustered.

Nearest Neighbour Index = 2 × D × √ (N/A)

D = the average distance between each point and its nearest neighbour

N = the number of points under study

A = the size of the area under study

* Alternative formula: Observed Mean Distance / Expected Mean Distance

The formula produced by the nearest neighbour analysis produces a figure expressed as the Nearest Neighbour Index which measures the extent to which the pattern is clustered, random or regular.

Figure 19 – Interpretation of Nearest Neighbour Index

Examples: Analyze patterns – Nearest Neighbor Index

Search the Nearest Neighbour and its distance – the nearness principle (the least-effort principle)

Nearest neighbour search, also known as proximity search or closest point search is an optimization problem for finding closest points. Formally, the nearest-neighbour search problem is defined as follows: given a set of points in space, find the closest neighbour for a given point.

One type of GIS analysis is finding out which features are closest to a given feature. Using nearest neighbour, you can find out which points from one layer are closest to which points from another layer. You can also find out which points are closest to each other in the same layer.

“A person who is given various possibilities for action will select the one requiring the least expenditure of effort”. – the last-effort principle.

According to Darcy Kim Rossmo, crimes often occur in relatively close proximity to the home of the offender. While criminals are mobile, they don’t seem to go very far in committing a crime. A majority of crimes appear to take place within a mile of the criminal’s residence. Time is seen as a commodity and almost all people act in a manner to conserve its use.

According to the least-effort principle, when multiple destinations of equal desirability are available, all else being equal, the closest one will be chosen.

It is important to remember that many factors come into play in the psychology and behaviour of choice. An individual’s perception of distance is influenced by several factors, including:

the relative attractiveness of origins and destinations;

the number and types of barriers separating points;

familiarity with routes;

the actual physical distance;

the attractiveness of routes.

Find the Nearest Neighbour

Let’s say we have a new criminal trend in the city: people have reported multiple cases of pickpocket in the street, in the last two weeks.

One method of approach would be to compare the locations of thefts with the residences of thieves known with this modus operandi (thieves recently released from prison or previously convicted for similar crimes).

Let’s say we have a set of points on a map, representing the places where people were pickpocketed; and a second set of points representing all the residences of suspects (thieves known with this modus operandi). We want to identify which is the nearest suspect’s residence for each crime that took place.

Using a nearest neighbour search, the GIS software would return a table with a row for each crime. Each row will contain two new values: Nearest Neighbour ID and Distance to nearest neighbour. In this scenario, the nearest neighbour would be the nearest suspect’s residence.

The next step would be to join this table with the table containing data about the suspects. After the join is complete, you can see for each crime which is the nearest suspect’s residence. (Figure 25).

The fields that the join will be based on are Near field ID (NEAR_FID) from Crimes and Object ID from Suspects.

Generate Near Table

Let’s say we have a set of points on a map, representing the locations where a suspect stopped his car, being suspect for drug dealing; and a second set of points representing all the video recording cameras in the city.

We want to identify all the cameras in a 100 meters’ radius of our suspect’s car stops and the distance for each one.

The GIS software has a function which will automatically generate a new table, containing the name of the video cameras in the selected radius (100 meters) and the distance calculated from the location of the car stop.

After generating the table, it is also necessary to do join operations, in order to bring the columns containing the names of the video cameras and the descriptions of car stops (figure 27).

Analyse patterns – Spatial Autocorrelation

Spatial autocorrelation is another term for spatial dependency. It is more complex than one-dimensional autocorrelation because spatial correlation is multi-dimensional (i.e. 2 or 3 dimensions of space) and multi-directional. In GIS, Spatial autocorrelation is applied to polygons.

Moran’s I index is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. It is a global statistic that shows whether the pattern is clustered, dispersed, or random. An intensity value is assigned to each aggregate point and requires some variation in the values for this statistic to be computed. Neighbouring areas that have similar values are reflected in high Moran's I values.

In figure 29, the white and black squares are perfectly dispersed so Moran's I would be −1. If the white squares were stacked to one half of the board and the black squares to the other, Moran's I would be close to +1. A random arrangement of square colors would give Moran's I a value that is close to 0.

index closer to +1 indicate clustering;

index closer to 0 indicate random pattern;

index closer to -1 indicate dispersion.

Difference between Nearest Neighbour Index and Moran's I. Index:

Spatial autocorrelation in GIS helps understand the degree to which one object is similar to other nearby objects. Geographer Waldo R. Tobler’s stated in the first law of geography: “Everything is related to everything else, but near things are more related than distant things.”

Spatial autocorrelation techniques used in law enforcement, assume that criminal events that occur in different locations (yet in close proximity) are related. Positive spatial autocorrelation suggests that “areas with high crime rates are clustered together, and areas with low crime rates are clustered together”. If high values at one area are associated with high values at neighbouring areas, the spatial autocorrelation is positive and when high values and low values alternate between adjacent areas, the spatial autocorrelation is negative (e.g., a checkerboard model).

To understand how Moran’s index works, let’s look at figures 30, 31 and 32 and compare how a clustered, random and dispersed data model looks like on the map of Bucharest.

In figure 30, on a scale from -1 to 1, Moran’s I index is equal to +0.74; The index has a high value, because areas are geographically correlated, regarding crime rates. Areas with high crime rates are clustered together and areas with low crime rates are also clustered together. This means that we can act using GIS to analyse this type of crimes.

In figure 31, Moran’s I index is equal to -0.00; this means that the areas are not geographically correlated and crimes are randomly positioned in relation to each other. These types of crimes are not geographically dependent, so they don’t give us a pattern to work with.

In figure 32, Moran’s I index is equal to -0.83; this means that the affected areas are precisely dispersed in relation with each other. This means that we have a pattern of dispersion, revealed using GIS tools.

In this case, only those polygons (squares) which counted more than 5 offences (coloured in orange) were considered affected zones. Moran’s I index was calculated taking in consideration if a polygon is affected or not; the numbers were not taken into consideration.

Practical exercises

After connecting to the data folder “GIS LVL 2 Data” using the Catalog, you will need to bring to your workspace the data needed from this folder. Don’t forget to set the right coordinate system (HTRS96 Croatia TM) for your workspace. When you bring data to your workspace, keep in mind that the source data coordinate system should be the same as the workspaces coordinates system (you can use project function in order to convert data).

After joining the administrative data with the points of interest (in this case police stations) based on spatial location, you will obtain an attribute (count) which represents the number of points of interest in that specific administrative unit. With that data, using “symbology”, you can create a thematic map based on the number of points in each administrative unit.

After creating the map, you can classify the theme based on standard deviation of the data (using classification – method – standard deviation).

After creating the desired map, you can use a normalisation value (in this case we will be using shape area, but you can use population or other similar values) in order to obtain a more realistic map, based on values.

After creating this map, you can add labels in order to better understand the description of the map.

Using “Mean center” function, you will obtain the geographic center (or the center of concentration) for the set of features.

Using “Central feature”, you will obtain the most centrally located feature in a point, line, or polygon input feature class (don’t forget to use euclidean distance).

Using “Standard Distance” you will obtain the standard deviation of the distance of each point from the mean centre.

Using “Standard Deviational Ellipse” you will be able to see if the distribution of features is elongated and hence has a particular orientation.

Using the date set “Zagreb_Offences_Proj_D2” which represents the offences committed in September 2016 (fictional data) in Grad Zagreb, you can determine how frequent some crimes are, based on date, weekday, type of crime, number of victims, day time, etc by using the “frequency” function.

By using this function, you will obtain tabular data with the frequency of attributes you have selected.

Using the “create fishnet” function, you will be able to do the basic steps in quadrant analysis. This functions generally creates a fishnet over the geometric form you want, and just like in thematic map, you can use colour ramp in order to see which quadrant has the most points of interest (or crimes, depends on the data you have).

Don’t forget to give the new feature class a name, input a cell size width and height (in this case 10.000 meters), uncheck create label points and in geometry type select polygon. After the process is done you can check if the fishnet was drawn according to the geometry of our area of interest by using drawing order. Just like in thematic mapping, join the quadrants with the number of points and using colour ramp, represent the squares according to the count attribute.

Nearest neighbour analysis provides a basic test to identify whether there are spatial patterns in the data and what the nature of these patterns might be. Unlike quadrat analysis, it uses distances between points as its basis. In order to see if these patterns exist, use “Average Nearest Neighbor” function (don’t forget to check the “Generate Report” checkbox). In order to see the report you can go to Geoprocessing – Results and open the last activity done from current session.

Moran’s I index is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. It is a global statistic that shows whether the pattern is clustered, dispersed, or random. An intensity value is assigned to each aggregate point and requires some variation in the values for this statistic to be computed. Neighbouring areas that have similar values are reflected in high Moran's I values. In order to see this, use” Spatial Autocorrelation (Moran I)” function and for example we can use this on “Zagreb_Offences_Proj_D2” and use as input field the number of victims (don’t forget to check the “Generate Report” checkbox). In order to see the report, you can go to Geoprocessing – Results and open the last activity done from current session.

Hot Spots

Crime Hot Spots

What is a hot spot?

Areas of concentrated crime are often referred to as hot spots. Researchers and police use the term in many different ways. Some refer to hot spot addresses (Eck and Weisburd; Sherman, Gartin, and Buerger), others refer to hot spot blocks (Taylor, Gottfredson, and Brower; Weisburd and Green), and others examine clusters of blocks (Block and Block). Like researchers, crime analysts look for concentrations of individual events that might indicate a series of related crimes. They also look at small areas that have a great deal of crime or disorder, even though there may be no common offender. Analysts also observe neighbourhoods and neighbourhood clusters with high crime and disorder levels and try to link these to underlying social conditions.

Though no common definition of the term hot spot of crime exists, the common understanding is that a hot spot is an area that has a greater than average number of criminal or disorder events, or an area where people have a higher than average risk of victimization. This suggests the existence of cool spots—places or areas with less than the average amount of crime or disorder. It also suggests that some hot spots may be hotter than others; that is, they vary in how far above average they are.

One of the first geographical questions that are asked of crime data is "where are the hotspots?”. A hotspot is a geographical area of higher than average crime. It is an area of crime concentration, relative to the distribution of crime across the whole region of interest (e.g. a city centre, census ward or tract, municipal district, county or state). Hotspots are often clusters of crime that can exist at different scales of interest. Knowing where these hotspots of crime are located offers a first step when exploring why these areas may suffer from persistent problems. However, what may initially appear as a fairly straightforward process of mapping crime data and identifying its hotspots can actually be quite challenging and prone to interpretation error. GIS software products offer a variety of techniques for representing spatial patterns, and the functionality between GIS software products may differ, such that what may be possible in one application may be different in another. Many GIS are also supplied with application extensions that offer a range of additional functions for visualizing crime patterns.

It is worth appreciating that hotspot mapping is not a beauty contest over which map looks the best – a visually stunning hotspot map does not explain why crime occurs at a location. However, good cartographic design is important in hotspot mapping as it clearly identifies areas that persistently suffer from crime. A visually appealing map can help enable a more focused approach to understanding areas that require crime reduction resources, and can offer direction for initiating the next analytical stages that explain the problem and how it can be tackled. Hotspot map are therefore a blend of good cartographic design and robust methodology, and are a first step towards exploring crime patterns in more detail. The theories that are discussed in this chapter help in understanding why crime incidents concentrate at certain locations, and provide the important basis for thinking about the actions that are appropriate when applying and designing reduction initiatives and policing strategies to hotspots. When mapping crime and analysing spatial patterns it is important to not lose perspective of these theoretical principles. Certain important geographical principles of spatial analysis are also presented in this chapter to ensure that the identification of crime hotspots is as accurate and effective as possible.

When is a hotspot 'hot'?

A question that often arises in hotspot analysis is how to define a map area as "hot". There is no universal or standard numerical threshold that can be used to define the number of crimes that need to have occurred in an area for the area to be defined as "hot". Hotspots are relative to the area under study. In other words, a hotspot represents an area of high crime concentration, relative to the distribution of crime across the whole region of interest.

Point maps

The most common method for displaying geographic patterns of crime is by point mapping. This method is popular because it is a simple digital way to carry out a familiar and traditional method of crime mapping: placing pins representing crime events onto a wall map. The figure next shows a sample of robbery and residential burglary data as point maps. As you view the images, ask yourself which areas you would identify as the three main hotspot areas in the figure. If you were to ask a colleague to identify the three main hotspot areas, it is likely that they would identify different areas or that the size and shape of the coverage of the area that they identify as a hotspot would be different. So who is right? At this stage answering this question is actually quite difficult. These maps demonstrate that it is difficult to clearly identify the location, relative scale, size and shape of hotspots when crime data are presented as points. The large volume of data that are mapped makes it difficult to visualise and interpret accurate patterns in the data's spatial distribution. An additional problem is that certain locations on the map appear to be single crime points but may in fact be multiple events mapped on top of each other. This occurs when crime events at the same location have been geocoded to exactly the same coordinates.

While point maps do have crime mapping value when only small numbers of crimes are to be displayed, they can be misleading when identifying hotspot areas, are not the most visually descriptive examples of hotspot maps and may not be the best map design to enthuse discussion and gather interpretation from others. When it comes to handling large data volumes, a point map can become easily cluttered, especially if these points are also labelled with attribute information. Points mapped at coincident locations can be repositioned by scattering the points around their common location, but this introduces error in the location of crime events. It is usually better to use a symbol of variable size to represent the differences in the number of crimes at each location. For example, a graduated size symbol map could be used to identify properties that are repeatedly burgled. Care needs to be taken when interpreting maps of this type because the size of a symbol may be large enough to obscure patterns in surrounding areas. It is also possible that the size of the symbol is so large that it does not exclusively cover the precise location where the crime occurred, and so may lead map readers to falsely interpret where a crime happened. A large symbol can suggest that neighbouring locations were the target of repeated crime events.

Geographic boundary thematic mapping

Thematic mapping is a very popular technique, yet there are a number of geographical tyrannies associated with this technique that can lead to misinterpreting the geographical distribution of the underlying crime data.

Geographic areas of various sizes and shapes, when aggregated and thematically shaded can be misleading. For example, natural tendency is for the map reader's attention to be drawn to the large areas that are boldly shaded (MacEachren; Monmonier).

Thematic mapping is a process that shades the whole of a region and can often be too coarse to represent the detailed spatial patterns of actual crime events. Indeed, it is highly unlikely that crime events are uniformly spread throughout a region. This becomes clear when examining, which shows the hotspot area that was marked as area C in the next figure. At this more detailed level of inspection it is possible to see that the distribution of the crime data across these geographical areas is not evenly spread, and that there are large areas where there are no crimes. The thematic shading gives the impression that crime is spread over the whole area. Although commonly done by crime mappers, most cartographers would consider it unacceptable to map raw counts of crime to areal units. The appropriate approach, when dealing with polygons of different sizes, is to divide the number of crimes by some appropriate denominator, such as the number of houses (for burglary) or the number of residents in an area (for robbery).

A second problem that affects all types of thematic mapping is the MAUP. This is where the results of any geographic aggregation process, such as the count of crimes within a set of geographic boundaries, may be as much a function of the size, shape and orientation of the geographic areas as it is of the spatial distribution of the crime data. In essence, when thematically mapped, different boundaries may generate different visual representations of where the hotspots may exist.

A third point to consider is the class boundaries that can be set for the thematic map. In general, classes should be organized so as to be as easy to understand as possible. In many cases it is useful to apply a custom range, where each range break is logical. The map should be the central message, and if the audience question the legend that has been used, then this can distract attention away from the message that is being presented with the map. A logical range setting (e.g. 0, 1-5, 6-10, 11-15, Greater than 15) can be easier to understand than the majority of other settings (see Harries, 1999 and section 12.5.1 for more information on class boundaries).

Grid thematic mapping

A technique that can help overcome the problems of varying sizes and shapes of geographic areas is to use a uniform grid, where each cell (a quadrat) is of the same size and shape. Each grid cell can have a crime count associated to it, which can then be thematically mapped. The mapped value could also be a density value calculated from the count and cell area.

Choosing an initial grid cell size is difficult. An initial guide can be to use one that is approximately the distance in the longest extent of the map, divided by 50. For example, if a study area's longest extent is 10 km distance, an initial trial grid cell size to use would be 200m.

Most GIS software includes tools for the creation of these types of grids. Once the grid is created, a point-in-polygon operation can calculate the number of crime points in each grid cell. The grid can then be thematically shaded in relation to the count of crime points within it. Figure 6.5 shows the thematic grid maps of the robbery and residential burglary sample data, and areas A, B and C have been marked as the likely crime hotspots. When compared to the three respective hotspot areas, differences between the areas that were selected are revealed. Both maps use the same data, but the techniques have identified certain different distinctions.

Grid thematic mapping does tend to better represent the spatial pattern of crime when an appropriate cell resolution has been set, in terms of determining the location, size and relative scale of hotspots. However, grid thematic mapping does suffer from certain similar problems to all thematic mapping in that it can still be affected by the MAUP. A coarse series of grid cells may hide some of the spatial patterning detail within the cell and that inappropriate class boundaries for the thematic map can produce unhelpful or misleading results. Many crime mappers also often comment that they do not like the appearance of grid maps, in that the 'blockiness' can be distracting. Improving the granularity by reducing the cell size does help to identify some of the high crime areas in more detail, but can often only have the effect of losing much of the visual patterning of crime that a slightly coarser grid offers. It also comes at a cost of larger file sizes and processing time.

Continuous surface smoothing methods

An increasingly popular method for visualising the distribution of crime and identifying hotspots is one that creates a smooth continuous surface to represent the density or volume of crimes distributed across the study area. These types of methods are commonly referred to as interpolation techniques and include inverse distance weighting and kriging. These types of techniques use an intensity or population value taken from sample locations to estimate values for allocations between sample sites. An example of this is a continuous surface map that is used to represent the distribution of rainfall, where the values between rain measurement points (the sample sites) are estimated from a function that considers the rainfall readings at these points and the distribution of these points.

With crime data we do not necessarily have sample sites where there is an intensity value, and neither are we trying to estimate the number of crimes that may have occurred between these crime point locations. We should therefore avoid methods that aim to create estimated intensity values in the gaps between our points. Instead, surfaces that we wish to create to represent the distribution of crime should tell us something about the density or clustering of crime points at all locations in our study area.

A suitable method for visualising crime data as a continuous density surface is quartic kernel density estimation. Eck and colleagues describe the method as follows: The quartic kernel density method creates a smooth surface of the variation in the density of point events across an area.

The method is explained in the following steps:

• a fine grid is generated over the point distribution;

• a moving three-dimensional function of a specified radius visits each cell and calculates weights for each point within the kernel's radius. Points closer to the centre will receive a higher weight, and therefore contribute more to the cell's total density value (figure bellow); and

• final grid cell values are calculated by summing the values of all kernel

estimates for each location'.

The cell values that are generated typically refer to the number of crimes within the area's unit of measurement (e.g. crimes per square kilometre).

The quartic kernel density estimation method is available in most GIS software as extensions (e.g. HotSpot Detective or Vertical Mapper for Maplnfo and Spatial Analyst for ArcGIS) and is also available in CrimeStat. It typically requires two parameters to be entered before it can be applied against crime data. These are the grid cell size and bandwidth (also known as the search radius or 'interval'). Of these, bandwidth is the parameter that will lead to most differences in output when it is varied.

A search radius (or bandwidth) is selected, within which intensity values for each point are calculated. Points are weighted, where incidents closer to the centre contribute a higher value to the cell's intensity value of the cell.

Bandwidth selection

Choice of suitable bandwidth has seen much discussion, both from the statistics field and also from spatial epidemiology, where kernel density estimation has been widely applied (Hogg; Bowman; Cliff and Haggett; Bowman and Azzalini). For example, one method makes use of a Moran's I correlogram to examine how spatial autocorrelation changes with distance. The correlogram shows the shape of the distance decay as well as the distance upon which it approaches the global Moran's /. Using this method, the shape of the distance decay can indicate the type of kernel to select, while the 'sill' (the point at which the correlogram approaches the global Moran's /) can indicate an appropriate bandwidth (Cliff and Haggett; Levine).

However, this method cannot be applied on point data because the calculation of Moran's 7 is dependent on data being aggregated to geographic units. For point data, Brimicombe suggests values for the bandwidth to be 6,9 or 12 times the median nearest neighbour distance, while Bailey and Gatrell explain that 'the value of kernel density estimation is that one can experiment with different values[of the bandwidth], exploring the surface… using different degrees of smoothing in order to look at variation in [the surface] at different scales'.

One method for choosing the bandwidth value for kernel density estimation on crime data, suggested by Williamson, was to vary the bandwidth relative to different order values of the mean nearest neighbour distance. These different orders refer to the mean nearest neighbour distance between each point and either its closest nearest neighbour, it’s second closest nearest neighbour or its nth closest nearest neighbour (often referred to as different orders of K). These nearest neighbour distances for different orders of K can be calculated using software such as ArcGIS. Using a bandwidth value that relates to the spatial distribution of the crime points has the advantage of retaining a spatial component in the calculation of a density estimation surface, rather than selecting an arbitrary number as the parameter value. However, using a K-order mean nearest neighbour distance approach still requires a decision as to which K order to apply, meaning that its selection could still be quite arbitrary.

Following on from Bailey and Gatrell's suggestion, a useful rule to follow is to consider the geographic scale at which crime hotspots need to be identified and choose a K-order mean nearest neighbour distance that will best reflect this scale. Low K orders are best applied when the crime mapper wishes to visualise crime patterns in fine detail, for example to identify specific localities (e.g. street corners) that have high crime levels. Larger K orders will more heavily smooth point data to provide a more general view of the distribution of crime, and could be used for more strategic purposes such as identifying neighbourhoods that require strategic crime reduction investments. It may be clear from this that more research is required from the crime mapping field, research that identifies the affect the bandwidth has on the accuracy of hotspot mapping output and the interpretation of the images, rather than just determining bandwidth based on what looks the best. In this section we will demonstrate the impact that bandwidth size has on the visual output generated from kernel density estimation.

Using the kernel density estimation method also requires specifying the cell size of the fine grid that is initially generated across the crime series distribution. Large cell sizes will result in more coarse-looking maps but are suitable for large scale output, while smaller cell sizes will offer a finer level of granularity more akin to a continuous surface, but may generate large file sizes. Where the user is unsure over the cell size to use, we suggest following the methodology of Ratcliffe where cell size resolution is the result of dividing the shorter side of the minimum bounding rectangle (i.e. the shortest of the two extents between the maximum x and minimum Jt, and maximum y and minimum y) by 150. Although an arbitrary value, it works as a reasonable starting point for most crime mapping applications.

The rise in popularity of kernel density estimation as a way to visualise spatial patterns in crime data has been largely due to its availability in software packages, and the visual appeal in the outputs that can be generated to represent crime hotspots. A kernel density estimation output allows for an easier interpretation of where crimes cluster in comparison to point, geographic area thematic, and grid thematic maps. The maps area thematic, and also reflect more accurately the location, relative scale and spatial distribution of crime hotspots in comparison to these other methods. The kernel density estimation method also considers concentrations of crime at all event levels, rather than grouping some crime events into clusters and discounting others – an issue that was identified in some of the early crime hotspot mapping techniques such as STAC. The kernel density estimation method also creates grid cell value outputs that can be compared from map to map (assuming the same parameters are employed). Finally, the method has the advantage of deriving crime density estimates based on calculations performed at all locations and retains some practical flexibility in map design.

Issues in the use of kernel density surface estimation

Certain problems do exist with the kernel density estimation method. First, kernel density estimation is a smoothing technique where the level of smoothing is determined by the bandwidth. This can result in surfaces that smooth over and into areas where no crime has happened and where no crime point data exists (such as just outside a study area), and hence exaggerate the distribution of the crime problem. The issue over which class boundaries to choose to represent the different thematic thresholds also still presents itself as a problem. Many of those who use the technique often fail to question the validity or statistical robustness of the map that is produced, being caught instead in the visual lure of the image. As a result, little regard is given to the legend thresholds that are set. For example, a map showing the distribution of crime as a kernel density estimation surface can have a variable number of hotspots depending on the ranges selected by the map designer to show spatial concentrations of these point events.

In essence, by setting a lower threshold for the highest colour value on the map, the crime analyst can give the impression that there is a higher crime problem in an area than there may be in reality.

Chainey suggested the application of incremental multiples of the grid cells' mean to help standardise thematic thresholds. Whilst this approach can help determine useful thematic thresholds, the approach does require some careful calculations for it to be applied. What is still missing is a method that can statistically define those areas that are hotspots. The kernel density estimation method can produce some excellent results in identifying the location, size, shape, relative scale and orientation of hotspots, but care must be taken in the selection of thematic range settings. After the following case study, the next sections explore statistical methods of hotspot detection.

Local Indicators of Spatial Association (LISA) statistics

From a crime mapping perspective, spatial association statistics test whether the number of point events in an area is similar to the count of point events in neighbouring areas. Moran's I (a technique already discussed in Chapter 5) is one such test. It explores the spatial autocorrelation between data variables (i.e. where events that are close together have similar values than those that are further apart) and can determine if positive spatial autocorrelation is said to exist.

However, these global statistical measures may offer little insight into the location, relative scale, size, shape and extent of hotspots, and often only summarise an enormous number of possible disparate spatial relationships in crime data.

In recent years a number of local statistical processes have been developed, processes that identify the association between a single value and its neighbours up to a specified distance from the point. These statistics are suited to the identification of hotspots and can be used to identify distances beyond which no discernible association exists (Anselin; Getis and Ord; Ratcliffe and McCullagh). In addition, a problem with the mapping techniques that have been discussed so far in this chapter is that none of them can define with any statistical significance those areas that are suspected of being hotspots. Local statistics can offer additional statistical robustness to support the suspicion that certain areas can be defined as hotspots. These LISA statistics include Local Moran's I, Local Geary's C and the Getis and Ord Gi and Gi* statistics.

All these LISA statistics assess the local association in data that is mapped, but do so in different ways. The Local Moran's / is based on covariance, the Local Geary's C is based on measuring differences between points and the Gi and Gi* statistics compare local averages to global averages. It is the Gi and Gi* statistics that have received most attention in recent years by crime mappers because as a method they fit neatly with the definition of a hotspot – they identify those areas where the local averages (e.g. concentrations of crime) are significantly different to the global averages (i.e. in comparison to what is generally observed across the whole study area).

Gi and Gi* statistics

The use of the Gi and Gi* statistics is best demonstrated with an example. We will use an area subdivided into regions, shown as a 16 x 16 cell grid shown in the figure bellow. Each cell can be identified by its centroid point (positioned in the centre of each cell) and each cell has a count of the number of crimes in that area (figure below). In our example, the centroid distance from each cell to another is an arbitrarily chosen value of 125 m.

A 16×16 matrix of cells, each holding a value representing the number of crimes within their respective areas. In this example the distance between each grid centroid is 125m

Consider the point positioned in the eighth row of the eighth column in the figure above. This point (which we shall call i) has the value 9. In the first instance we specify a null hypothesis that site / is not the centre of a group of unusually high values centred on i and its surrounding cells (neighbours). We can use standard terminology and call each neighbour j, such that our null hypothesis states that the total crime count in i and a group of j cells up to a distance d from i is not significantly higher than anywhere else on the grid.

This null hypothesis states that the sum of values at all the j sites within a radius d of i is not more (or less) than one would have expected by chance given all the values in the entire study area (both within and beyond the distance d}. If local spatial autocorrelation exists, it will be exhibited by a spatial clustering of high or low values. This can be determined by Gi or Gi* statistics. When there is a clustering of high values, the Gi and Gi* values will be positive. Low values will yield a negative Gi or Gi* value.

Anselin, Getis and Ord, and Ratcliffe and McCullagh provide details of the equations for Gi and Gi*. We will not worry about looking at them in this chapter, but instead will focus on how we can apply these statistics to crime data. The difference between the two statistics is that the Gi* statistic also includes the value of the point i in its calculation. Gi excludes this value and only considers the value of its nearest neighbours (all of the cells) against the global average. Gi* is the more popular of the two statistics because it considers all values within d.

Geographical Information Systems software such as ArcGIS and Maplnfo routinely offer these types of spatial statistical analysis functionality.

The Gi* statistic requires two parameters: the lag distance and the number of lags to apply. A lag distance is the radius of a moving circle that visits each grid cell. In many ways it is similar to the bandwidth measure that is used for kernel density estimation, except that a suitable value is easier to determine. The lag distance should be at least the distance between each grid cell, and preferably at least the distance of the radius from each cell's centroid that has a coverage that will consider all of its immediate neighbours. The distance between the grid cells in the example 16 x 16 cell grid in the previous figure is 125m. A suitable lag distance to apply could be 178m as the furthest distance to one of the eight immediate neighbours is 178 m (i.e. V(1252 + 1252)). As we will test for local clustering we should determine an appropriate distance. To ensure that all eight of the immediate neighbours were included within the first lag, the lag distance was set to 180m. Increasing the number of lags allows a crime mapper to explore how far spatial association exists from each point. A lag of 5 for the 16 x 16 matrix will calculate Gi and Gi* values within a distance (d) of 180m, 360m, 540m, 720m, 900m.

Table below shows the Gi* statistics for the cell positioned in the eighth row of the eighth column with the crime count value of 9. Higher positive values of Gi* indicate greater clustering of high values. At a lag of 1 the Gi* statistic is positive. This high and positive Gi* statistic indicates that there is positive local spatial association between this cell and its neighbouring cells. That is, this particular cell and the eight cells immediately surrounding it and forming a 3 x 3 matrix have a high total count and that the high total in these cells is greater than the global average.

The Gi* statistic at a lag of 2 is also positive but not as high as the Gi* statistic at a lag of 1. The Gi* value remains similar up to a lag of 4 (i.e. up to a distance of 720m from the cell in question), but then reduces considerably to 0.3 at a lag of 5. For those cells that have low values (i.e. low crime counts) and which are also surrounded by cells of low values, the Gi* statistic would be negative.

To legitimise the Gi* results it is possible to determine a threshold measure that defines whether these values are statistically significant. Ord and Getis suggest a Bonferonni-type test to generate measures of significance. (Bonferonni is a statistical procedure that performs multiple tests to determine levels of significance in a data sample.) Ord and Getis62 publish a comprehensive table for Gi* and Gi at the 90, 95, 99 and 99.9% significance levels. A common significance level to use is 95%. Figure 6.12, derived from Ord and Getis62, summarises the Bonferonni generated 95% significance levels for a range of sample sizes.

Gi* statistics for the cell positioned in the eighth row of the eighth column of the 16 x 16 grid. At a lag of 1, within a distance of 180 m from this cell, there is a high positive level of local spatial association. This reduces at a lag of 2, remains stable to a lag of 4, but then reduces close to zero at a lag of 5.

The 95% significance level for the sample of 256 records is approximately 3.55. This means that there is significant statistical evidence of crimes clustering (i.e. there is a hotspot) at the cell positioned in the eighth row of the eighth column of the 16 x 16 grid, up to a lag 1 distance. This means that the cell is at the centre of a cluster of high cells, a cluster that would only occur by chance if the values in the 16 x 16 matrix were randomly scattered around the matrix less than 5% of the time. This type of result provides a distinct advantage over the previous techniques that have been explored in this chapter for identifying and mapping hotspots: it identifies those areas that can be statistically defined as 'hot'. Figure 6.13 shows those cells that display statistical evidence of local spatial association above the 95% significance level at lag 1. In essence, these are the statistically significant hotspots in this grid of cell-based aggregated crime data.

The Gi and Gi* statistics can be applied against simple crime counts or where the grid's cells contain other values that relate to the underlying crime data, such as kernel density estimation values for each cell.

Figure 6.13 Cells in the 16×16 matrix grid that show statistical evidence of local spatial association above the 95% significance level at a lag distance of 180m. The distance across each cell is 125 m

A problem sometimes associated with the kernel density method is that in some locations it may smooth across or into area where there is no recorded crime, because it is not constrained to the high detail of the underlying geography of the crime point distribution. Crime mappers sometimes have to explain to police officers why there is an apparent crime level (i.e. shading) in an area where no crime is possible. An advantage of the Gi* technique is that as it compares local averages against global averages. Therefore areas where it is impossible for certain crimes to happen (e.g. for residential burglary this would include reservoirs, rivers or any areas where there was no residential housing) can be identified in a GIS and the cells that cover these areas could be extracted from the full grid coverage so they do not influence the global average. Secondly, the kernel density estimation may smooth away the peaks in areas where large bandwidths aggregate high values with neighbouring low values. This can be seen in Figure 6.14 where areas identified as hotspots from the Gi* results are not grouped in the 'high crime density' threshold on the kernel density estimation maps. This, however, may be a small price to pay for the increased readability of a kernel density estimation map, or can be corrected for with a Gi* derived output.

Summary

Hotspot mapping, like all forms of mapping, is a naturally iterative and experimental process (i.e. the first map that is generated may not be the one that is finally used). Care needs to be taken in the selection of parameters to ensure that what is being identified as a hotspot is accurate. Hotspot mapping also requires good cartographic skills, and although it is not a contest to find whose map looks the prettiest, sound cartographic principles are important if the message that the map conveys is easy to interpret by its reader. This chapter has explored the application of a number of techniques for identifying hotspots. The discussion was not to necessarily identify the optimum technique but to explain and understand the strengths and weaknesses in those techniques that are in common use by crime mappers. Several more advanced techniques have also been presented, and whilst there are others beyond the realm of this book, our focus has been to explore methods which are currently available for use in policing, crime reduction and crime prevention.

Practical exercises

Using the data given, you can determine the distance between points in order to determine which point (crime) is closer to a point of interest (police stations). In order to do this, you have to use “Point distance” function. In this example, you will determine which crime was committed to the closest police station. You can use a search radius in order to have the search not extending further than that inputted distance (in this case 1000 meters).

The result will be a table in which you will have a unique id automatically generated, an input field id (which is the id of the crime), a near field id (which represents the id of the police stations) and the distance between these points (distances lower than 1000 meters in this case). In order to have the full set of data, you can join the new table with the table of offences and the points of interest table (police stations).

In order to measure the degree of clustering for either high values or low values using the Getis-Ord General G statistic use “High/Low Clustering” function (don’t forget to check the “Generate Report” checkbox). In this example we will be using Zagreb offences with the victim number as input field.

In order to identify statistically significant hot spots and cold spots using the Getis-Ord Gi* statistic you can use “Hot Spot Analysis” function.

For an enhanced and smother visualization, you can use “IDW” function which interpolates a raster surface from points using an inverse distance weighted technique.

If you want to calculate a magnitude-per-unit area from point features that fall within a neighbourhood around each cell, you will use “point density” function.

If you want to perform hot spot analysis of a point or polygon feature class you can use “Optimized Hot Spot Analysis” function. The result will be a representation similar to the fishnet one.

In order to calculate a magnitude-per-unit area from point or polyline features using a kernel function to fit a smoothly tapered surface to each point or polyline, you will use “Kernel Density” function.

In order to return the minimum, the maximum, and the average distance to the specified Nth nearest neighbour (N is an input parameter) for a set of features use “Calculate Distance Band from Neighbor Count” function (for this example we will be using the first neighbour). The result will be statistically with no graphical representation.

In order to measure spatial autocorrelation for a series of distances and optionally creates a line graph of those distances and their corresponding z-scores you can use “Incremental Spatial Autocorrelation” function. Z-scores reflect the intensity of spatial clustering, and statistically significant peak z-scores indicate distances where spatial processes promoting clustering are most pronounced. These peak distances are often appropriate values to use for tools with a Distance Band or Distance Radius parameter.

Mapping and Analysing Change over Time

Introduction

Crime is a dynamic event. The incidence of crime is neither stationary over space nor stationary over time. While CIS provide practitioners and researchers with a remarkable tool for mapping crime over space, the development of temporal analysis tools has lagged behind the development of spatial methods. This chapter explores ways to examine temporal and spatial-temporal patterns of crime across different temporal scales and aims to equip the reader with not only a range of tools but also an understanding of the value that a temporal understanding can contribute to the crime reduction effort. An appreciation of the temporal characteristics of a crime pattern can go a long way to preventing and reducing crime.

Much of this book has until now concerned itself with the production and application of single crime maps: fundamental tools in the description of criminal behaviour and crime patterns. When determining a crime reduction strategy, understanding the changing mosaic of criminal behaviour over time becomes equally as important. First, it is useful to know if an observed crime pattern is steady in space over time or moves from place to place. Offenders occasionally curtail their activities in one area and find new targets in response to police activity, a process referred to as 'displacement' (Barr and Pease; Hesseling). Secondly, once a crime reduction strategy has been implemented, it can be useful to evaluate the strategy in order to determine if there has been a reduction in crime in the target area as well as to test for the existence of any displacement. This type of work requires the crime mapper to have at their disposal a range of analysis tools that are applicable to exploring patterns not just spatially, but also temporally. The development of temporal crime mapping tools has tended to lag behind the expansion of spatial techniques. This chapter will introduce a number of techniques that can map crime patterns in the temporal dimension.

While most people readily grasp the three dimensions of space, time is an altogether more difficult aspect to work with. We cannot touch it, nor can we see it, yet we know just how concrete and real it is when assignments are due, deadlines loom or we are late for a train. Crime information is usually recorded with day and time attributes. The degree of precision of the temporal information determines the temporal resolution available for analysis. Temporal resolution can be best described as the minimum difference between two independently measured temporal values that can be distinguished by the analytical method applied. More complex analysis is possible with call for service data, often recorded to the second or minute, than with the movement of glaciers which have a temporal resolution measured in years. The temporal resolution determines the minimum level of temporal analysis that can be conducted, but does not inhibit longer time analysis.

Data recorded to the minute could be analysed on a minute by- minute temporal basis, though it may not reveal much useful intelligence. However, the same data could easily be analysed on an hourly or daily basis, allowing variation during the course of a day to be seen. Crime data that only record the day of the offence limit the minimum temporal resolution to daily frequency counts at best.

Time can be displayed using a simple notation – the letter t with a subscript number that is used to indicate a time component. For example, f0 is used to signify either the first in a series of temporal values or the value at the present time. Moving forward into the future increases the number (t1,t2,t3…tn), while past values are shown with negative values (t_1, t_2, t_3…t_n). Vasiliev identified five categories of temporal information (moments, duration, structured time, time as distance, space as clock) of which the first four are most relevant to crime analysis. To these relevant four, we add another that is particular to crime mapping – the time span. In the following section, these categories will be shown against a timeline, a method for visualising time.

The timeline

The timeline is a useful tool with which to visualise the different temporal categories. We tend to think of time as having distinct periods that end at the commencement of the next period (days, hours). Periods of time, such as weeks or seconds, are convenient tools to help people communicate information. Real time is not constructed of distinct blocks of time that run together, but is a continuum, and we can visualise this continuum as a timeline that stretches into the past and into the future.

Temporal categories

The figure bellow (first row) shows a timeline for five hypothetical burglaries carried out by one offender. If offences are recorded temporally as moments, then they would appear on the timeline (second row) as individual events with no duration, happening at particular points along the timeline. The actual duration (third row) of each offence differs depending on how long the offender spends in each property. Both of these can be measured relative to familiar structured time units, such as hours (fourth row). If we could interview the burglar, we may discover the patterns of behaviour (fifth row). These would show that the burglar travelled on foot to most offence locations, returning home after each one. Most offences were within a few hundred metres of the burglar's home, but travelling on foot has a significant time penalty which influences the range of possible targets as well as the number of burglaries that could be committed. The last offence was committed with the aid of an accomplice's car that enabled the burglar to travel to a location much further than before. The final row shows the time span as reported to police. In the first two examples and in the fifth offence, the homeowners were away from the home for at least an hour. They were also away during the offences with short time spans, but their property was unguarded for a shorter time. We describe these temporal categories in more detail in the following section.

The timeline for five hypothetical burglaries. The five events are shown as moments along the timeline, though the duration shows that some burglaries took a longer time to commit than others. The structured time shows the fixed interval durations of hours during the day. Time as distance shows how far the offender travelled from home address to burglary site and how long it took to get there and back. The last offence was committed with the aid of a car, so the time to cover a much larger distance is relatively shorter. The final row indicates the time span of the offence start and end times as reported to police, shown in grey to indicate the range of possible times of the offence (in order to distinguish the actual offence duration, shown in black). The duration is the best indication of actual offence time, but is rarely available to crime researchers

Moments

A moment is usually expressed as a simple time expression, where a crime event is known to have happened at a particular time or is attributed with an estimated time. An event usually denotes a change in state of an object. In the case of a residential burglary, the object (the residential address) can be thought of as changing from a state of unburgled to burgled. When mapped as a moment, the event has just one temporal attribute – the time it happened. These types of event are easy to map. For example, a map of all calls for service to a police station in one day can show the location of each incident with the time of the call mapped next to the point. At some scales the point is not necessary, and the time stamp is enough to show the time and location. The ability to map the temporal pattern is determined by the temporal resolution available. If the crime recording system is only able to record the hour of the call, trying to query this system to map all incidents in a 10-minute period will be unsuccessful. Moments are usually depicted along a timeline (previous figure) as points with no length.

Duration

Duration is an indication of the length of time that it takes for an event to occur. For example, an intelligence officer might use surveillance data in court to show that a burglar took six minutes to steal from a property. Duration can also become a search parameter indicating the temporal extent of a query. With a map of all calls for service in one day, the day in question becomes the duration for the query that generates the map data. Events with a measurable duration are usually depicted along a timeline (previous figure) as lines with a length determined by the duration.

Structured time

Structured time is a basic mechanism of human activity that enables people to effectively communicate temporal change. Although time is a continuum, it is helpful for us to be able to describe when and how long events take place in terms of seconds, minutes, hours, days, weeks, months and years. There are of course smaller periods of structured time than seconds, and longer periods than years; however, the range from minutes to years is the general area of concern for crime mappers. It is worth noting that conversations involving structured time often implicitly involve some rounding of time. For example, if an intelligence analyst says that a known burglar has been active for a couple of months, then it is often the case that the offender has actually been active for a slightly longer or shorter period of time. Structured time is depicted on timelines as lines with equal length and spacing.

Time as distance

Time can be used as a measure of distance. A light year – the distance light travels in one year – is not of much use to a crime analyst, but from a crime theory perspective it can be useful to consider time as a spatial factor in the movement of offenders and the resulting patterns of crime. If, for example, an offender is required to report to a police station in New York every evening, the offender is unlikely to be responsible for a pattern of rapes in San Francisco. Space is something that offenders often have to cross to reach their target, and it takes time to cross that space. The concept is also useful for some operational policing functions. The placement of police stations and vehicles can be optimised for emergency response by mapping the location of hotspots of calls for service and factoring in the time it would take to travel to the location.

Time span

Time span is a temporal category that is fairly unique to crime mapping. It has evolved from the realisation that the actual moment and duration of many crime events are not known. These temporal categories only come to light, if ever, when offenders are caught and interviewed. The reality of modern law enforcement is that many offenders go undiscovered and the only available information at the time of the crime report is when the victim last saw their property in a good condition, and when they returned to find their property missing or damaged. Many police databases record these variables as the/rom date and time and the to date and time. They can also be called the start and end date and time. The period of time between the from and to times is called the time span, and it represents the duration within which the crime event happened. Within the time span, the event occurred as either a moment or duration. Offences which have a recorded time span, but do not have a distinct offence time, often create analytical difficulties. The distinguishing characteristic of the time span compared to other temporal categories is the ability to reflect the degree of uncertainty of an event. Even though this reflects a lack of knowledge about a criminal incident, it does not mean that the crime analyst does not now have enough information to understand patterns of criminal activity. The section of this chapter on aoristic analysis has a method for analysing such offences.

Temporal resolution and querying a temporal database

When mapping crime incidents, the scale of temporal resolution becomes relevant. The more precise the data, the more precise the mapping potential is. A crime database that only records the date of offences can be queried in terms of calendar time, but not in terms of clock time, when the time of the offence on the day in question is recorded. Recording the time of offences or calls for service dramatically increases the range of analysis options.

For example, when mapping all calls for service to one police station in one day, the query (or search) duration of the map is the 24-hour period. On such a map, each incident could be plotted as a point with a fairly precise temporal representation. Display options for this type of map include colour coding each point to represent each hour of the day, or replacing the point symbol with text to show the time of the call (for example, 1245 or 12:45 pm). Other possibilities include classifying the point symbol by police shift. The incidents become moments with a time span of a single minute, and the day becomes the search duration. However, if the temporal resolution of the map changes, so do the subsequent map characteristics. If we change the search parameter to a year, a map of all calls for service in one year that shows each point as a time of occurrence will more than likely swamp the display with numbers or symbols. With such a map, the temporal resolution of the moments becomes untenable, and a more appropriate cartographic solution for displaying the calls for service must be found. More often than not, point mapping becomes inappropriate at this resolution and kernel density estimation surface maps or other mapping techniques become necessary.

Figure 3.1. Chronological temporal classes and thematic temporal classes shown along the timeline.

Before mapping any change in crime patterns over time, it is necessary to interrogate a crime database in order to be able to select the correct subset of the data. There is little point in mapping 10 years of crime when the task only requires a map of new offences since last week. A given search duration of crime events will result in the return of a number of incidents from a crime database. This is the most basic form of a temporal query and is one with which most crime researchers are familiar: find all burglaries that happened in 2003, or find all robberies that happened from midnight to 6 am. This raises two possible cartographic options for simple crime mapping. First, it is possible to map offences in a chronological fashion so that offences that happen close to the same time as other crimes will be in the same class. A second option is to map offences that happen around the same shift or time each day. This mapping approach is more thematic than chronological. These two options are shown as a timeline example in Figure 3.1.

When performing a temporal query on a crime database it is necessary to anticipate the type of question to be asked. Simple questions regarding 'what happened' and 'when' are easy to determine (though 'when' can be difficult for crime that is recorded as a time span and requires special treatment – we address this later in this chapter). More advanced spatiotemporal questions relate to questions of change. Peuquet identified three classes of spatio-temporal query:

One class of query addresses change in an object or feature. For instance, has an offender moved house in the last year? Where was the suspect living six months ago?

A second class of question addresses the nature of a spatial distribution over time. For example, where is the highest intensity hotspot for burglary this year compared to last year? Which police district has the highest number of drug arrests since March?

A third class examines temporal variation in multiple phenomena. Questions of this nature could include asking if nearby major sporting events are associated with an increase in local car crime, or are assaults associated spatially and temporally with bar-closing times.

To address these more complex queries it is necessary to consider the range of possible temporal relationships between crime events. This becomes especially important when evaluation of crime reduction strategies and police operations takes place because it is often necessary to demonstrate the spatio-temporal location of crimes before, during and after an intervention in order to determine the success (or not) of the strategy. It is also a factor with crime events recorded with start and end (or from and to) times.

Peuquet69 recognised seven temporal relationships, as shown in Figure 3.2. Some of these can be converted into crime-specific illustration queries, as the following examples show:

• Select all crimes that occurred prior to the police operation (X before Y).

• Select all crimes that happened on Tuesday and select all crimes on Wednesday (X meets Y).

• Select all robberies that happened as the convenience store closed (X ends Y).

• Select all burglaries with a start time before 6 pm and an end time after 6 pm (X overlaps Y).

• Select all murders that happened during 2003 (X during Y).

Figure 3.2. Temporal relationships. Source: Adapted from Peuquet.

Designing the appropriate temporal query is a prerequisite to spatiotemporal mapping. Once completed, there are different techniques that can be used to address different mapping problems.

Temporal questions

There are generally three important temporal questions that policy-makers, decision-makers and crime researchers ask. First, they are concerned with the degree of change of a temporal pattern: How has the distribution of offending changed since last month? Where are new crime patterns appearing? These questions address issues of pattern fluctuation and are answered by comparison of one distribution with another.

The second significant question is the problem of temporal magnitude: Which areas show an increase in crime? Where is the largest increase in crime? These questions can be a little trickier because they are not simply a matter of mapping the change, but also a matter of the magnitude of the crime in an area. For example, a police district which has one robbery a month will show a 100% increase if robberies go up to two a month. This 100% increase appears to be substantial; however, it pales next to a district that only has a 5% increase in robbery, but which moved from 100 robberies a month to 105.

The final type of question is becoming more common with the current move towards intelligence-led policing and problem-oriented policing: Has a crime reduction strategy made a difference? Again, this requires the crime mapper to compare past and present crime distributions, but also to seek a determination that any measured change is significant. The remainder of this chapter explores different spatio-temporal mapping methods that help to address all of these questions.

Aoristic analysis

Towards the start of this chapter, time span was identified as one of the five temporal characteristics. The time span represents the range of possible times over which an offence could have occurred. It is often necessary to use a time span technique with property offences such as burglary and auto theft when the victim left their house or car for a few hours and returned later to find the crime had happened while they were away. The range of hours (or, in some cases, days) during which the offence happened at some point is referred to as the time span. Aoristic analysis (Ratcliffe and McCullagh; Ratcliffe, 2000, 2002) is a spatio-temporal tool that calculates the probability that a crime event occurred within a given time period within the time span. It has been designed to assist with the analysis of offences where it is not possible to determine the actual time of offence.

The difficulty that can occur with offences of indeterminate time is best illustrated with an example. Consider three burglaries that occur at residential premises over the course of a weekend. In the first burglary, shown as (a) in Figure 4.1, the owners left their home at midday on Friday only to return on Sunday morning to discover the burglary. In the second burglary, the victims left the home on Saturday morning and returned on Sunday morning (b). In the third offence, the victims were away from the home for a few hours during Saturday (c).

Figure 4.1. Three burglaries (a, b and c) shown along the timeline. Tick marks are indicated at every two hours on the scale

So what can be said about the number of offences that occurred on Saturday? It can be said that one definitely occurred on Saturday and two others may have. Another alternative is to estimate a proportional value of each crime based on the portion of the offence time span that falls within Saturday. Offence (a) has a time span of 46 hours, of which 24 fall within Saturday. If a crime can only occur once and can therefore be given a value of 1, we could allocate 0.52 (24/46 = 0.52) of the offence probability to Saturday. This can be expressed as either 0.52 or 52%. Offence (b) has a time span of 20 hours, of which 14 falls within the temporal range of Saturday, resulting in a value of 0.7 (70%). Add these values to 1.0, to represent the one crime that definitely occurred on Saturday (c), and we can say that the aoristic value of Saturday burglaries is 2.22.

The spatial dimension

The aoristic value for each offence can be visualised and further analysed spatially. Most of the techniques in this book consider that the value of each offence that is mapped is one. That is, an offence happens once and has a value of 1.0 for the purposes of any calculations. This value can be adjusted by the aoristic weight to permit an analyst to map offences by the probability that the crimes happened within the temporal parameter of the map. In other words, a simple map with a title of Saturday burglaries could show the three crimes as point symbols, coloured or shaded according to their aoristic value. For example, this can be achieved by shading offences with a value of 1.0 as the darkest shading, reflecting the certainty that these offences happened in the time period being examined. Other offences would be shaded according to the probability that they occurred on that day. This approach would increase the accuracy of the map by reflecting the possibility that some offences may have occurred outside the map's temporal limits of 'Saturday'. For completeness, the symbols that had aoristic values of less than 1.0 should appear on other maps, coloured or shaded accordingly. For example, the offence labelled (a) in Figure 4.1 would appear on the Friday, Saturday and Sunday maps, if these were produced.

This concept is illustrated in Figure 4.1.1., where a three-dimensional representation of offences in a study area is shown. The timeline is expressed as the vertical access, and four offences are shown. Three have start and end times that are far enough apart that they exist as possible offences in both of the two temporal snapshots, t1 and t2. The long time span of these offences means that they have relatively low aoristic values. There is one offence that only appears in the t1 snapshot. This crime, with a relatively short period between the start and end time, has a high aoristic value, signified by the darker colour at the intersection of the spatial location and the temporal dimension.

Figure 4.1.1. Aoristic spatial-temporal values expressed in three dimensions

Practical exercises

In order to observe the change over time, of crime evolution for example, you will have to compare 2 categories of the same type. In this case, we will be using Zagreb crimes, and split in 2 categories by time, the first category will be crime that happened in the first half of September, and the second category with the crimes that happened in the second half of September.

Create a hotspot using “Kernel Density” for each period of time.

Remember to use different colour ramps (different colours recommended).

Vs.

Display both hotspots on the map, and then assign a transparency value (properties – display window) to the one on top (20% would be sufficient).

As a first conclusion, we observe that the main hotspot is slowly decreasing in length, but the southern hotspot is expanding.

You can represent the path in time someone took. From the given dataset geocode suspect_locations.xls file.

After adding the points to the map (with the correct coordinate system), use “Points to line” feature, which will create a chronological path.

This path is one single line. In order to have segments for each time record, we will have to split the line, to do this, use “Split line at point” function. After using this function, you can edit the symbology to “Arrow at end” in order to better see the direction.

After this you can calculate the speed for each segment, given the fact that you know that each point on the map is generated at every 5 minutes. For this you will have to create a new attribute.

In order to see the most frequent places he passed through and where he spent the most time, you can make a kernel representation.

As a conclusion, you can observe that he is walking based on segment speed until he enters the park, he looks like he is searching for something, afterwards he is spending lots of time in one specific area, and then he starts to run, based on his speed per segment, which leads us to the conclusion that he is running away.

To better observe the motion in time, you can use the time slider, after enabling time on point’s layer (in this case use time attribute).

Remember to access options panel and set the playback speed to slow in order to better observe the path in time. After having the best options set, you can export your work as video or sequential images.

You can use time slider to observe how crime has been adding up in time (Zagreb crimes in September).

If you check the “Display data cumulatively” the streaming video will show you the crimes from day one adding then the data from day two, next frame will add the data from day three, and so on.

If you don’t check “Display data cumulatively” it will display only the data from day one, the next frame will show the data from day two, third frame will show the data from third day, and so on. This is very useful if you want to export as images 30 days of crimes without having to do selection for each day.

A way to express time as distance is through buffers. For example, let’s say a missing child has been reported. From the place, he has been reported, you can use buffer zones in order to set the search perimeter. So, let’s say for the first search radius (30 minutes since he was gone) we will be using a search radius of 1000 meters, the second buffer (1 hour) the search radius will be 2000 meters, the third buffer (2 hours) the search radius will be 5000 meters (the distances/time are just for example). To do this in one single move and not do buffer after buffer, you can use “Multiple Ring Buffer” feature and directly input all the buffer limits you need.

Spatial Theories of Crime

Introduction

Crime mapping is all about the geography of crime and, as Patricia and Paul Brantingham noted in 1981, there are four dimensions to every crime:

1. a legal dimension (a law must be broken);

2. a victim dimension (someone or something has to be targeted);

3. an offender dimension (someone has to do the crime); and

4. a spatial dimension (it has to happen somewhere).

They defined the spatial dimension as a place in space and time where an offence occurs, and these are components of the crime equation that can be mapped. We now have GIS to help us plot criminal activity, and techniques that you will read about in this book can map the temporal component as well. However, what can we possibly discern from mapping crime? If crimes were a random occurrence that had an equal chance of happening anywhere at any time then there would be no point in mapping criminal activity. There would be no evidence that future crimes would occur in the same place as past crimes, and there would be no opportunity to predict the potential locations of offenders. However, this is not the case and the following chapter will explain why crime is not randomly distributed across space but is concentrated into hotspots of activity.

Readers with a background in geography may well feel an urge to skip a chapter that proposes to discuss criminological theory. Similarly, crime prevention practitioners may feel some agreement with Marcus Felson and Ron Clarke when they said that 'criminological theory has long seemed irrelevant to those who have to deal with offenders in the real world'. Indeed, many criminological theories provide little practical insight into effective crime reduction. A number of criminological theories concern themselves with what motivates individuals to commit crime. For example, Robert Merton argued, through the notion of Strain Theory, that deviant behaviour is caused by a social system that holds out the same goals to all its members, yet at the same time does not give members of that society equal means to achieve those goals. Though theories such as these are interesting, they are often difficult to convert into a practical crime reduction strategy from a policing or practitioner perspective. After all, it is difficult to tell just by looking at people walking past on the street how divorced they are from their means to achieve their life goals and who therefore might be a potential offender. However, a solid appreciation of why crimes occur where they do and the spatial behaviour of victims and offenders will help the analyst better understand crime in society; how individuals can protect themselves; how communities can prevent crime; and how the police can detect and solve crime.

The main theoretical area that underpins crime mapping is a practical subset of mainstream criminology called environmental criminology. This has nothing to do with oil spills in Alaska, but is the study of criminal activity and victimisation and how factors of space influence offenders and victims.

This chapter begins by exploring how the importance of this spatial influence on people came to be recognised, before examining the spatial dynamics of offenders and the interaction of the offender and victim in time and space. The chapter will conclude with a look at some of the different ideas that have circulated to improve crime prevention and detection, resulting from a greater understanding of criminal behaviour across time and space.

The space and time of offences

Any police officer knows that the distribution of crime is not uniform across either time or space. There are hotspots of activity. For example, if you wanted to pick a hotspot for a drunken brawl then sometime around midnight in an area with a high density of bars would be a pretty good bet. While it may be simple to guess the likelihood of some offence patterns, explaining why they exist is a different matter. The drunken brawl example might be easy, but how do we explain why some areas are plagued by burglary while others see little burglary but are awash with vehicle theft?

Certain theories can help us understand these patterns. These theories do not just consider the risk of crime, but also cover offender behaviour. After all, if the crime patterns are not random then the offenders cannot be acting in a random way. It is of course true that some criminals will break the mould and do things differently, but the majority tend to act in a predetermined manner. These tendencies to react in a similar way to the same opportunities across space are termed aggregate criminal spatial behaviour.

Figure 2.1. Hourly probability of burglary in the Australian Capital Territory, 1999-2000. Source: Ratcliffe (2001).

Some offences have clear patterns. For example, while Hollywood would have us believe that residential burglary is committed by offenders creeping round the house in the middle of the night, residential burglary actually tends to occur in the middle of the day. This is demonstrated in Figure 2.1. The patterns of residential burglary over a typical day in the Australian Capital Territory peak in the early afternoon to mid-afternoon hours. This contrasts to non-residential burglary which Figure 2.1 shows is the reverse time pattern. These patterns are confirmed for other countries (for example Sorensen, and the interviews with offenders conducted by Rengert and Wasilchick and Cromwell). Why might these patterns occur? The following sections examine theoretical explanations for offence patterns and the offender and victim behaviour that cause these types of patterns.

Routine activities

Routine activity theory originally started as a macro-level explanation of predatory crime, but has progressed over the years to provide a worthwhile mechanism to examine criminal opportunity and crime prevention in a variety of settings. The original work examined changing patterns of employment and the new criminal opportunities that are created when there are fewer people staying at home during the day. The simple idea is that behaviour of victims explains the occurrence of crime, and that for a crime to occur, three components are necessary.

There must be the presence of a likely offender, the presence of a suitable target and the absence of a capable guardian. These three components must meet in time and space to formulate the necessary 'chemistry' for crime. Note that there is no discussion of a target necessarily being a person. The practical nature of this approach is that buildings, cars, mailboxes, people or a wide variety of objects and things can be targets. There is also no clear definition of what is construed to be a capable guardian. This could mean a person, as in the usual meaning of guardian, such as a police officer, security guard or even shopkeeper, or could also include CCTV surveillance systems. Routine activity theory does not just discuss offenders, targets and guardians, but adds the important, but often forgotten, qualifiers. Not all offenders are likely offenders, as some will lack the technical knowledge and skill to attack certain types of premises. In a similar vein, not all targets are suitable targets, as they may be inaccessible (such as rooftop apartments) or too well-defended. As said, many objects and people can be guardians; however, at different times they may not be capable guardians. Researchers in Scotland noted that CCTV cameras worked to prevent criminality most of the time, unless the offenders were under the influence of alcohol when they did not care about the cameras. The thinking behind routine activity theory is that the risk of crime changes over time with the movement of people throughout the daily routine activities of their lives. We will discuss this in more detail in a later section of this chapter. For the moment, routine activity theory can be summarised by the following simple equation:

Likely offender + suitable target – capable guardian = crime opportunity

Most researchers take the existence of likely offenders as a constant in our society and attempt to explain and prevent crime by examining the two remaining components of the equation. Crime prevention practitioners may therefore examine the possibilities for introducing suitable guardianship into an area as a way to prevent crime or to make existing guardians more suitable.

Enhancements to routine activity theory

Most of the early work in this area concentrated on the nature of targets and guardians; however, some developmental ideas regarding offenders have taken place. Whether an offender will be a likely offender can depend on the presence or influence of 'handlers'. A handler is a person, a third party, who can influence the behaviour of the offender.

A parent may therefore be a handler, as could a teacher or any other person who knows or who could determine the name of the person. This makes sense. Would a person commit a crime in the presence of someone who might know them and who could tell the police? A handler may also be a person whose respect the offender might not wish to lose. While the handler may not tell the police, they may not approve of criminal behaviour. In this way, a school friend or work colleague can become a handler for a potential offender.

While a handler has some influence over an offender, a guardian has some influence over the likelihood of crime occurring. Remember that guardians can be formal, such as police officers, or informal, such as the presence of a friend as company on the walk home at night. These two types of controllers provide control: handlers control offenders and guardians protect targets. John Eck has since introduced a third type of controller – the place manager. A place manager is someone who is able to control a place even if they are not formally in charge of the area. Certain individuals have the capacity to discourage crime in particular areas. These people include landlords, street stall owners, store owners and ticket clerks. With place managers, we now have three types of controllers, and to summarise in the words of Marcus Felson, 'Crime opportunity is the least when targets are directly supervised by guardians; offenders, by handlers; and places, by managers'. This can be depicted visually with the crime triangle (Figure 4.1.). The crime triangle helps to focus analysis and problem-solving towards the causes of crime, from a routine activity perspective, and the mechanisms that can influence those causes and so prevent crime.

Figure 4.1. The crime triangle

The spatial arrangement of attractive targets

Target suitability can change over space and time. While routine activity theory provides a general model with which to consider the likelihood of crime occurrence, even available targets can differ in their attractiveness to a criminal. During his time studying at university one of the authors was the proud owner of a 15-year-old, clapped-out Citroen 2CV car. It was usually left unlocked, often with the window open, in one of Nottingham's highest vehicle crime areas, yet it remained untouched. Apparently Nottingham car thieves have no appreciation for classic French engineering, and it shows the reality that some commodities that are available to steal are not attractive to offenders. Ron Clarke examined records of stolen property and summarised the basic characteristics of a suitable, or hot, target. Working from Cohen and Felson's VIVA (Value, Inertia, Visibility and Accessibility) acronym, he expanded the idea of hot products to cover most property offences, suggesting that a hot product is 'CRAVED' in that it is:

Concealable – things that are difficult to conceal are harder to steal. Offenders may be stopped by the police if seen carrying goods down the street, and shopkeepers will notice if large items are being carried out of the store.

Removable – the easier a thing is to remove, the greater the chance that it will be a hot product. Given that theft is the appropriation of property belonging to someone else, the necessity to take it to another place is fairly important.

Available – burglars do not spend much time in a house as this is when they are most at risk of capture, so objects that are visible and not secured are most at risk.

Valuable – this appears to go without saying; however, valuable is a relative term. Young offenders will target goods that they define as valuable, and this can include clothing and sports footwear. These goods are not necessarily for resale, so the value of items is dependent on whether the offenders will use the items themselves or sell them on.

Enjoyable – it may seem strange, but burglars tend to steal televisions, videos and CD players rather than kitchen items, even though these have a similar value. The degree to which a product can be enjoyed marks its potential theft risk – an indication of both its value to the offender and possibly its resale value on the stolen goods market.

Disposable – many items are stolen so that they can be sold or traded to others, therefore disposability is an important characteristic for stolen goods. Some, but only some, stolen goods are traded for drugs, and these items are usually sold on again, creating a lucrative stolen goods market.

So how can we explain crime patterns with these ideas of hot products and routine activity theory? Ratcliffe examined crime patterns for vehicle crime in the eastern suburbs of Sydney, Australia, and found that vehicle crime in the affluent suburbs near the beaches was focused during the overnight periods. The residents in this area are generally wealthy with expensive cars, and expensive cars are most definitely 'craved', having a high value for both joyriding (enjoyable) and resale or 'ringing'. Ringing is the process of creating a new apparently legitimate vehicle by altering the documentation of a stolen car (also termed 'rebirthing' in Australia). Although the Eastern suburbs are an affluent part of the city, the density of housing means that few residents have space for private garages. Vehicle crime is therefore concentrated into the overnight period because the items are CRAVED, they are suitable targets at night (the cars are elsewhere during the day) and the night time hours provide for few capable guardians. Attractive products are not distributed evenly throughout urban space. Given that some offenders are known to work with 'fences' who can provide a ready market for stolen goods, some items are stolen to order. Professional car thieves will tend to target affluent suburbs in search of specialised vehicles, while a joyrider or car thief in the early stages of his career may search a less wealthy suburb in the hope of finding an older car that is easier to steal and less conspicuous. Beyond car theft, most white-collar crime is concentrated in the central business district as this is where the major financial institutions can be found.

Rational choice

All of this might appear to suggest that offenders will take any opportunity to steal anything and everything that is not chained down! Well, this may be the case for a few offenders, but most make some sort of a decision to commit a crime by weighing up some of the pros and cons. What are the rewards, against the chance of being caught? This suggests that to commit a crime is a (fairly) rational decision and that an offender will commit an offence while trying to achieve some sort of desire or goal. The goal may be to derive personal gain, as in burglary or theft, or personal pleasure, as in the crime of joyriding. If the legitimate means of obtaining that goal are not available, then a decision may be made when a criminal opportunity becomes available. As Rengert and Wasilchick noted after their interviews with 31 burglars, 'the decision to commit burglaries was a purposeful, rational decision in almost every case'.93 The decision may not be one that is fully calculated, as offenders may not weigh up all of the consequences. Interviews with younger offenders generally find that they do not consider the implications of capture (Fleming; Shover), though some criminals will consider the risks in their choice of criminal behaviour. For example, vehicle crime is often seen as attracting lower penalties from the criminal justice system than burglary.

It is argued that criminal decision-making is in two parts. There is a long term, multistage decision to become generally involved in criminal activity (criminal involvement decision) and a shorter-term, more immediate decision (the criminal event decision) to grasp an opportunity that is presented. Of course, factors such as drink, drugs, peer-pressure or limited education do mean that not all offenders' decisions are purely rational, resulting in what has been termed 'limited rationality' also known as 'bounded rationality'.

These terms are an acceptance from researchers that some offences are committed with less-than-military planning behind them. Although the effects of drugs and alcohol can limit the rationality of offenders, the immediate decision-making of a burglar (for example) is primarily based on the environmental cues from the prospective target, cues that can change from place to place: can the offender be seen breaking in, is there anyone home and is there an easy way into the house? This characteristic, termed rational choice perspective or rational choice theory , provides a framework to consider offender decision-making when a crime opportunity is presented. It can also be used to consider likely strategies that will influence the decision-making of the offender.

Situational crime prevention

Crime prevention is a huge field and, in modern society, a huge business. One of these is situational crime prevention, possibly the most spatial crime prevention concept and one that is a natural geographic corollary of rational choice theory. Situational crime prevention does not worry about why people commit crime, but concerns itself with preventing the opportunities for crime. It suggests a number of opportunity-reducing tactics that are crime-specific, that involve manipulating the immediate environment in a systematic and permanent way, and that are intended to increase the effort and risk while reducing the rewards that are perceived by a range of offenders.

Geographical Information Systems lends itself to situational crime prevention studies due to the place-specific nature of the technique and the ability of GIS to deliver a spatial analysis. For example, Holzman and colleagues examined assault rates against women in two public housing areas in the US. The study used GIS to map assaults within the housing estates, determining that the architectural design afforded some offenders more privacy and accessibility than in other places and that this influenced the rate of assault against women. George Rengert and his co-workers went a stage further and designed a high definition GIS to map crime within the confines of a university campus (2001). A student survey of unreported crime was combined with crime recorded by the campus police to better understand the real pattern of crime across the university. They even went as far as to propose a method for mapping crime within buildings.

In providing a way to influence someone not to commit a crime, three main strategies are suggested by situational crime prevention. First, it may be possible to increase the risks. By making the chance of capture much higher, offenders may make a rational choice to seek a less well defended target. Tactics such as video recording customers at bank cash machines are an attempt to increase the risk of capture of cash card robbers. The cameras work by either recording the picture of the offender as they steal the card or cash from a customer at the machine, or by recording the offender when they try and withdraw cash with a stolen card.

A second method of influencing the decision-making of offenders is to increase the effort required to commit a crime. A number of new cars have multiple levels of security including alarms, engine immobilisers and tracking systems that tell police where to find the car (sometimes with the thieves inside). These situational crime prevention tactics (called situational because they often only work for that particular car or building) all work to increase the effort required to steal the car.

Finally, it is possible to reduce the rewards of crime. Again, situational crime prevention tactics such as tagging expensive clothes with tags that stain the fabric with a permanent dye if removed from the store, or by fitting mobile phones that require a secret personal number before they will operate, are all ways to reduce the rewards of crime.

Clarke initially proposed 12 basic techniques to situational crime prevention, with four techniques for each of the three core areas of increasing the effort, increasing the risks and reducing the rewards. These were later increased to 16 techniques, by including the concept that it is possible to remove the excuses for crime.. This area of crime prevention is continually developing, and a good way to keep up with the latest ideas is at the website www.popcenter.org.

Territoriality and defensible space

Not all crime control has to be toughened glass, barriers, CCTV and police officers. Crime can also be controlled more informally. Jane Jacobs recognised that increases in the number of people on the street on busy roads increases the number of potential witnesses to a crime and the number of bystanders who might intervene. The sheer volume of people acts as a crime inhibitor. Might it be possible to use this informal social control in a broader manner? To do so, the informal control must work by tapping into a spatial component of human psychology, that of territoriality. In residential areas, people seek some degree of privacy from the communal and public areas of our world. This private space is the last refuge, and an area that we seek to protect. Territorial functioning' is the mechanism by which we aim to exclude unwanted persons, through the use of boundaries, fences and other signals that indicate to others that a certain area is private and not for everyone to wander through.

Taylor has described human territoriality functioning as a system of attitudes, sentiments and behaviours that are specific to a clearly marked place. This system signifies that a group or individual has some expectation of excludability of use. In turn it also indicates a responsibility and control of activities in the specific location. From a spatial standpoint, Taylor concentrates on the face-to-face perspective and at the block level. And while there would appear to be limits on the extent of territorial functioning up to the suburb level, those who have a stake in a certain area, such as a small park or communal area, will police the area and care for it, looking out for troublemakers.

According to the main originator of defensible space, Oscar Newman, the catalyst that starts this active surveillance of certain spaces is a distinct demarcation between those areas that are deemed to be public and the areas that a group are prepared to defend. The private areas that are considered part of the territory of an individual or group become the 'defensible space' and are actively policed. Other areas, such as those that are clearly public or are 'confused space', areas where ownership is not clear to onlookers, tend to be ignored by the residents or occupiers. While Jane Jacobs examined the implications for urban planning, Newman viewed the problem through an architect's eyes, looking more specifically at building design. In the UK, these ideas were further explored by Alice Coleman106, who studied different crime types across various housing estates. However, it should be noted that the ideas of Newman, in particular, have been quite strongly criticised for producing evidence that is methodologically flawed or theoretically unsound. Indeed, while Newman recanted a number of his early ideas from the 1970s, there is no doubt that defensible space has certainly sparked debate regarding territoriality and how we view the space around us.

Crime prevention through environmental design

The work of Jacobs and Newman brought the spatial focus closer to home, to examine the immediate environment around the house. Around the home, after all, is where territoriality should be working at its maximum rate. But what about the workplace, or at school? C. Ray Jeffery expanded the spatial defensibility notion to promote ways of preventing crime in a wider range of areas. Crime Prevention Through Environmental Design (CPTED) is both the name of a book by Jeffery published in 1977 and a crime prevention philosophy increasingly adopted by researchers, practitioners and urban planners to consider the best designs of public and commercial areas to reduce criminal opportunity. CPTED (pronounced sep-ted) appeals to many working in the crime reduction area as it blends architecture, environmental criminology theory and urban planning in an attempt to reduce offending in public or 'confused' space.

Offender-offence interaction

Armed with an understanding of both offence patterns and criminal behaviour, it is now possible to start to build a model for the interaction between offenders and victims. This interaction must occur at some point in space and time, but can we explain why the victims were unlucky enough to meet the criminals then and there?

Crime pattern theory

While routine activity theory gives us a model to predict if a crime has all of the chemistry to occur, and rational choice perspective enables us to determine some of the thinking behind an offender's ultimate decision to commit a crime, where will the offence happen? We are now exploring the theoretical area that will interest many GIS researchers, because the interaction between the offender and the target has an inherently spatial dimension. The crime must happen somewhere, and that somewhere can be mapped and analysed.

A helpful convergence of routine activity theory and rational choice theory can be found in the area of crime pattern theory. This helps to bring the two areas of offender spatial distribution and offence spatial distribution together by examining the 'relationship of the offence to the offender's habitual use of space'. Crime pattern theory (sometimes also referred to as offender search theory) suggests that offenders are influenced by the daily activities and routines of their lives, so that even if they are searching for a criminal opportunity, they will tend to steer towards areas that are known to them. In their day-to-day activities they will be watching for targets that have no guardians or place managers.

Awareness spaces

Like offenders, all of us have various routine activities in our lives. Most of us have to go to work, college or school, and we usually go there from home. We may also go to shops and restaurants, bars and movie theatres. These repetitive journeys create within us a 'cognitive map' of places, routes and associations, and these cognitive maps become a general list of well-known areas, areas in which we feel comfortable. This environment consists of not just the physical things, such as buildings and subway stations, but also the social and economic infrastructure which we pass through. Cities become an urban mosaic to us, places where we have no knowledge, interspersed with well-known places. We also become familiar with the routes between these known areas. These islands of knowledge, and the routes that link them, become our 'awareness space' (Brantingham and Brantingham; Rengert and Wasilchick).

Like us, offenders also have awareness spaces. They also move between places such as work, school, shops and home, and for some offenders, the search for criminal opportunities takes place around these areas. Opportunities are not spaced evenly throughout a city, and some offenders will only be able to take advantage of some offence opportunities. Also, some of the awareness areas will not be conducive to crime due to the presence of guardians or place managers. Therefore for each offender we can generate a model of awareness space and criminal opportunity space (with the implicit absence of guardianship), and where they intersect we will find the areas of crime occurrence. Crime pattern theory is therefore strongly connected with the interactions of criminals and their physical and social environments. This hypothesis was modelled by the Brantinghams, an adaptation of which can be seen in Figure 3.1.1. Here we can see that awareness space consists mainly of the places that are routinely frequented, as well as the routes between those places. We may be more familiar with distant places that we frequent regularly than local places just around the corner that we never visit. Proximity does not always mean the same thing as familiarity.

The adaptation to the original Brantingham' model is in the inclusion of the location of friends as an influential component on offender awareness space. Although for most people, work or school plays a significant part in daily life; this can be less so for offenders. Costello and Wiles found that many offenders who could have been in the workforce had never had full-time employment, and Rengert and Wasilchick reported interviewing a number of offenders who had quit legitimate employment in order to pursue a professional criminal career, including one individual who made more money as a burglar than as a full-time computer programmer. These examples focus on residential burglars only; however, it is likely that the attractiveness in both lifestyle and income of a life of crime is probably more attractive than poorly paid legitimate employment for many burglars, drug dealers and robbers. Having a place of work is not a necessary requisite to forming an awareness space. The Sheffield study found that as many offenders had never been employed, they were often transient and heavily influenced by the location of friends and criminal peers.

Figure 3.1.1. Hypothetical model of the creation of criminal occurrence space where offender awareness space and opportunities coincide.

While we can see in Figure 3.1.1 that areas of criminal occurrence happen when awareness space and opportunities intersect, that is not the whole story. In the diagram we can see that some opportunities are outside the awareness space of the offender and are essentially unavailable, while some within the awareness space have variable attractiveness. For example for a residential burglar, all homes within their awareness space are theoretically potential targets, but some are more attractive than others. The areas with a greater proportion of targets that are potentially safer to burgle and more profitable will form part of the offender's 'search space' – as the opportunities area. Within this search space, certain targets will be more attractive than others, and the micro-search for a particular target occurs in the actual area targeted, termed the 'criminal activity space'.

Templates and cognitive behaviour

So why do some areas remain outside an offender's cognitive space, and why do they commit offences in familiar areas? Offenders' routine activities can be quite limited. In a study in Sheffield (UK), it was found that many offenders were unemployed, and indeed had never worked. This meant that they were often short of money. While this lack of employment and cash was probably a motivating factor in committing crime, it also meant that their routine activities were severely curtailed from a spatial point of view. They had no reason or resources to venture into unfamiliar areas, and their cognitive map was quite small as it did not include a workplace or many recreational opportunities.

There are several other reasons why offenders might commit offences in familiar areas. It is helpful to know the layout of an area so that if you need to make a quick getaway, you will not run straight up a dead-end street. Secondly, it has been suggested that offenders value feeling 'comfortable' in an area and not feeling as if they stand out. This has been suggested as a reason why offenders who live in poor neighbourhoods do not often commit offences in affluent areas. In a similar vein to the 'poor-rich' distinction is the 'white-black' neighbourhood distinctions found in the burglary patterns of offenders in the US. A number of studies have noted that black offenders avoid white suburbs and white offenders steer clear of black neighbourhoods, each group feeling that the avoided areas were unsafe (Rengert and Wasilchick; Wright and Decker). It is also interesting that the desire for spatial exploration to extend criminal opportunities is rare. Offenders are often constrained by time and financial resources and lack the freedom to explore other opportunities or to search further afield for fresh prospects.

While our daily patterns take us to school, work, shops, cinemas and home, we may also go to the coast for our summer holidays. If we do, then perhaps offenders also do. Yet if crime pattern theory suggests that offenders go to places that are known to them, why don't offenders regularly travel from the city to the coast to commit offences at the places where they take their summer holidays? At this point the least effort principle becomes a factor. Say, for example, that we need a carton of milk. There are lots of shops in the city that sell milk, but like most people we immediately consider the shops closest to home. To travel across the city and back just to get something that is available half a mile away is pointless. Buying a carton of milk from the nearest shop around the corner requires the least effort. The least effort principle comes into play for offender behaviour. There is no point in travelling 50 miles to steal a television when there is reasonable certainty that a similar television could be found in a house a few streets away. Physical space can be likened to a friction surface in that it requires effort to cross it. The further the distance to travel, the greater the cost in time and possibly money.

Travelling a greater distance to commit crime also incurs an additional possible penalty to buying milk. A person will not be arrested for walking down the street carrying a carton of milk, but a stolen television is a different matter. Increased distance to commit crime increases the effort, increases the risk and increases the possibility that the offender will stray into an unknown area. The least effort principle is a useful mechanism for thinking about offender behaviour, and is a fundamental concept behind journey to crime studies and geographic profiling, more of which will be discussed later.

It should be noted that crime pattern theory is a general theory to explain the crime patterns of offenders, and there will always be exceptions. Studies have found that a few offenders are influenced by others and do not commit crime within their own awareness space, either as a result of influence by people such as 'criminal fences' for stolen goods who direct the offender to new opportunities or by peers who introduce the offender to new areas. When this happens, the spatial pattern of offences can be very different. However, for the majority of offenders, the tendency is to offend in awareness spaces close to home. If all criminal patterns were purely random and individualistic, then we would not be able to draw conclusions about the behaviour of the majority of offenders. However, we know that broad behavioural tendencies do exist, and can be explained as aggregate criminal spatial behaviour.

Establishing a template

Environmental criminologists generally start from the assumption that offenders are motivated to commit crime. Their interest is in the choice of where and when. If offender behaviour was totally random, there would be little point in such work. However, as this chapter has shown, there is a considerable degree of predictability in criminal behaviour in space.

A degree of predictability also extends to the individual target selection. As the offender, either by prior design or opportunistically, comes upon a potential target, a decision is made to offend or not. This decision is based in part on cues that are perceived from the surrounding environment – cues that include physical, cultural and psychological characteristics. Prior experience of good and bad situations will influence the offender's interpretation of these cues, and the offender will compare the current situation with previous situations that were amenable to crime. These prior experiences form a template against which the existing circumstances are compared. As the offender commits the offence, he or she will often undertake the crime using the same or similar methodology to a previously successful criminal venture. After all, there is no point taking a risk with a new technique if an offender has an existing one that works. The process of actually committing the offence runs according to a 'cognitive script' that is based on previous positive criminal experiences. Both the establishment of a template and the creation of a cognitive script will tend to be fairly fixed once the offender has established a working methodology. It is the tendency to stick with what works that makes the study of offender modus operandi worthwhile.

From centrography to the journey to crime and geographic profiling

Some of the criticisms of the Chicago School over the years have included the blurring of criminal offender location and criminal offence location. This assumption, that crime and criminal are co-located in areas, confused the situation when data were aggregated and led to a number of subsequent studies that fell afoul of the ecological fallacy – the application of research findings from one level of aggregation to another. However, some geographers were beginning to explore criminal record data with an explicit understanding that offender residence and offence location are different places.

LeBeau tracked the behaviour of rape offence locations in San Diego between 1971 and 1975, examining the spatial change in pattern with centrography. This technique plots the change in the location of the mean centre of all points as well as examines the shape of the standard distance and standard deviational ellipse created when analysing the crime events to discern behaviour patterns. While Porteous had previously used centrographic techniques to determine gang territory in British Columbia, LeBeau enhanced the technique by tracking changes to the mean centre over time, concluding that spatial offence patterns change over time in different manners for rape types. He then went on to complete some of the earliest work using GIS to model individual offence patterns in relation to both time and offender residence. LeBeau concluded by raising the predictive benefits of spatio-temporal rape patterns, a theme worked on by Canter and Larkin.

Canter and Larkin' s British study of 251 sexual offences committed by 45 offenders in Britain proposed two models for the spatial behaviour of serial rapists. The commuter hypothesis proposed that one group of offenders, termed commuters, roamed out of their home range (the area around their residence) to commit offences in another area, the criminal range. In contrast, the marauder hypothesis speculated that a marauder would use the home as the base for offences, and would operate predominantly in the home range area. The commuter hypothesis therefore proposed that there would be minimal overlap between the home range and the criminal range, while marauders would demonstrate considerable convergence in their use of space. These hypothetical behaviours are shown in Figure 3.2.1.

Figure 3.2.1. The commuter and marauder hypotheses

Canter and Larkin went on to propose a circle theory to examine the distribution of their offenders. By drawing a circle using the two most distant crime events in an offender's crime series as the ends of the circle's diameter, they found that 87% of their offenders had a residence within the circle, supporting the marauder hypothesis for serial rapists in their sample. Although the circle hypothesis has been found to have limited application in crime detection, predominantly because the circle sizes tend to be extremely large and create a huge area for police to cover, the work helped to focus attention onto the predictive power of spatial patterns. At the same time, developmental work on both sides of the Atlantic were about to find an innovative application of crime pattern theory.

Kim Rossmo was a PhD student of Patricia and Paul Brantingham at the same time that he was also a police officer with the Vancouver Police Department. Around the same time, Professor David Canter was working on serial crime patterns in the UK. The centrography of Jim LeBeau had recognised the offender detection potential for a greater understanding of the spatial behaviour of criminals, and both Rossmo and Canter took this a stage further with a piece of reverse engineering. If an understanding of the home base and activity nodes of an offender could give some clues as to the likely offence locations, could it be possible to use the offence locations of an unknown offender to predict where the criminal might live?

To create a working methodology for this type of offender detection system, it was necessary to understand the importance of the journey to crime. There is often a theme to police drama television programmes. Over the course of an hour, the detective arrives in a quaint small town to investigate a grisly murder. The horrified locals are all sure the murderer is an outsider, but as the investigation progresses the focus turns inwards until in the last minutes of the programme the detective tracks down and exposes a local person who was the offender. These programmes play on a common theme – that our community is safe and anything nasty is the work of outsiders. However, as the detective often discovers (against the wishes of the townsfolk), the offender is usually local and has not travelled far to commit their crime. Journey-to-crime studies have repeatedly shown that, due to the least effort principle, offender-crime site distances are usually short.

Ratcliffe found that the average journey from an offender's home to a burglary target was about five kilometres (about three miles) for residential and non-residential burglars. This finding matches broad findings from the United Kingdom and the United States (Rossmo; Wiles and Costello). These figures are skewed by a small number of offenders who travel longer distances. In the Australian capital, Canberra, it was determined that one-third of burglaries are committed by offenders who have travelled less than a mile from their home address. Patterns for individual offenders show that as distance from home or other base increases, offending decreases. This pattern of behaviour is termed the distance decay effect (Rengert; Rossmo).

Of course, if this were universally true then every offender would steal from their next door neighbour. Many actually do, but this does increase the risk of being recognised and arrested. Some offenders therefore will limit the number of offences that they commit close to home, to minimise the risk of recognition by neighbours. This has the effect of creating a buffer around the home address. This can be seen in Figure 3.2.2. which shows a general model for offender behaviour. Note the distance decay effect as the number of offences drops off rapidly as distance from home increases. Also note that the buffer does not extend far from the home, and that offences still occur close to home within the buffer. The offending does not stop next to the home, it is just tempered by the possibility of identification.

Figure 3.2.2. Distance decay function with buffer

The criminal-spatial landscape

In an earlier section, we showed how offender cognitive behaviour formed a template which was used to judge potential criminal opportunities.

Awareness spaces are not just amoeba-like blobs, as you might have thought looking at Figure 3.1.1., but are made up of different structures which provide a changing pattern of opportunities to commit offences depending on the environmental backcloth – the social, psychological, economic, physical and temporal mosaic of the offender passing through urban space. These different structures change across space and affect the type of criminal opportunities that are available to the motivated offender.

Nodes, pathways and edges

In Figure 3.1.1. it can have been seen that awareness space is strongly influenced by the number and location of the nodes in a person's daily routine. A node, also known as an activity node, is a place that an individual is regularly drawn to, such as home, work or school. For offenders, nodes are also important as these areas tend to be the site of many of their offences. Searching for criminal opportunities in the immediate vicinity of a node is rare, and if it does take place then the search area tends to be quite small. A block or two from the node is more likely. As the young tend to commit more offences than other age groups, the type of node can also be a good predictor of crime. A fancy restaurant with fine cutlery and an expensive wine list may be a node for one select group in the population, but a fast food restaurant is more likely to be a node that attracts an age group in their peak offending years.

At some point, an offender has to travel from one node to another. The routes between nodes are pathways, and are also the locations of many offences. The type of crime and the opportunity may vary; but, from an aggregate perspective, pathways provide an opportunity to go past and assess new criminal opportunities. There can often be an increase in property offences near main street and arterial roads. The movement of offenders through the main roads provides an opportunity to explore a street or two from the main road. This exploration is rarely for more than a block or two, as it can be easy to get lost. Offending on, or near, the main road provides a quick escape route back to a familiar pathway. Of course, an offender may travel into the Central Business District by mass transit and not by private car. This reduces the burglary opportunity, but increases the possibility of other types of offending along a pathway. Robbery, pickpocketing or graffiti are associated with subway travel.

The third component of the urban landscape is the edges that exist between different parts of the city. As the Brantinghams140 note, these edges may be physical, such as the boundaries of commercial developments or the border between a park and a housing estate, or perceptual, such as the border between areas of different income or racial mix – a common feature of US cities. Perceptual edges may also be apparent in the territorial functioning (described earlier) of a group of neighbourhood residents. Edges can often provide criminal opportunities, because there is an expectation that outsiders are not usual on the periphery of areas. If they ventured into the centre of the neighbourhood then they are more likely to stand out and appear out of place. The rookeries of 19th-century London provided such an opportunity, by allowing a dense network of housing in which offenders resided to exist directly alongside the wealthy of the city of London. A shabbily dressed offender would stand out in the heart of the city of London, but might be expected to have strayed a street or two at the edge. The rookeries provided a bolthole in the event of police pursuit, as well as an administrative boundary, coming under the jurisdiction of the Metropolitan Police and not the City of London Police.

Crime generators and attractors

The spatial arrangement of crime generators and crime attractors is inherently tied to the nodes, pathways and edges of our urban world. A crime generator is a particular area or node where large number of people are drawn for reasons that are not related to any particular criminal activity that they might commit. These places are crime generators because they provide times and places where potential targets for criminal activity are concentrated into areas that are conducive to criminal acts. For example, shopping malls draw people who do not intend to commit crime or to be the victims of crime. The combined activity of lots of people drawn to the shopping mall provides an opportunity for the potential car thieves who are interspersed within the law-abiding citizens. These offenders may not be drawn to the shopping mall to commit crime, but find themselves suddenly faced with an unforeseen opportunity when they walk through a poorly lit and unattended shopping mall car park.

By comparison, crime attractors are places which create criminal opportunities and, in doing so, attract motivated offenders to the neighbourhood or suburb (or node). The lure of a known criminal opportunity draws offenders to the area, enticing them with the knowledge that the area has a reputation for a particular type, or types, of illicit opportunity. For example, red light districts offer the allure of prostitution, as in the area around Kings Cross in both Sydney and London; bar districts can attract individuals or groups looking for hard drinking and a fight; and street drug markets have an obvious attraction to addicts. The area can often draw in offenders from other areas (Brantingham and Brantingham, 1995, p. 8).142 The attractiveness of certain areas of the city for criminal activity is not a new phenomenon. Offenders are often drawn to the centre of cities, attracted to the features that have long been a part of big city life.

Spatial crime theory in practice

So how does this all fit together? Here we conclude by considering the behaviour of a single (hypothetical) offender and use this behaviour to summarise many of the key terms used in this chapter.

Smith is a committed offender, motivated and always on the lookout for an opportunity. This morning, he decides to go and see a friend. While walking to his friend's apartment he is scouting for opportunities. He knows that Mrs Jones across the road has seen the police come to his door many times and that she is suspicious of him, so he walks for a block so that she will not see if he gets up to something, moving through his buffer zone. At the local shops on the way, he sees some CDs on a display by the music shop door. The routine activities of the music shop owner provide an opportunity, as the owner is in the back of the shop and therefore not a capable guardian, Smith is most certainly a motivated offender and the CDs are suitable targets. They are concealable under his jacket, removable, available, valuable, enjoyable and disposable (CRAVED) as he may be able to sell them to his friend. However, just as he is about to grab a handful of CDs, the baker from the next shop comes outside to have a cigarette and acts as a place manager, removing the opportunity for Smith. Given the risk of capture, Smith makes a rational choice to try again another day. As he approaches his friend's house, he sees the cul-de-sac where a number of old people live. They are always tending their gardens, and have placed large potted plants down their street. He does not like to go down there as the residents tend to display quite a bit of territoriality. He once sat on a wall watching the old man at one house, when a neighbour came out and told him to go away or she would call the cops. With so much defended space, he decides to seek easier burglary opportunities nearby. He does not want to go far, due to the least effort principle, and he often visits his friend so this area is part of his awareness space. His friend lives in a fairly poor area, so Smith does not feel as if he stands out when he is in this area. Although he has committed some burglaries in this area, it is getting harder. He used to enter the apartment buildings and knock on all of the doors on a floor. If nobody answered, he would kick a door in. However, now the city council have provided some crime prevention through environmental design and made the entrances to the buildings security doors. The only one he can enter belongs to his friend, and he cannot steal from his friend's neighbours because they are all suspicious of him.

Smith and his friend go to the shopping mall. Their cognitive map of the mall says that there are lots of electronic and music shops on the upper level, a good opportunity for some shoplifting in the past. In the electronics shop, there unfortunately appears to have been some situational crime prevention to prevent shoplifting. The CD players are now behind a locked case, increasing the effort of theft. The notebook computers are for demonstration only and have most of their components removed, reducing the reward, and there is a security guard at the door, increasing the risk. They give up and go elsewhere. In the main foyer of the mall a crowd is gathering. Thoughts of crime gone from his head, Smith wanders over to see what is going on. A local singer is giving a show to sell CDs, but in the crowd Smith identifies a new opportunity. The crowd has acted as a crime generator because there are many open handbags. Smith's crime template knows that this is a good chance, and his modus operandi in the past has always worked. His cognitive script tells him to nudge a target from behind, and to steal their purse at the same time. He does this, apologises for the nudge (while pocketing the purse) and moves out of the crowd with his reward.

The stolen purse is full of credit cards, but Smith does not have the skill to make use of them. So he goes to a downtown bar to see another friend. On the way there, he takes a familiar bus route to the bar. He feels comfortable on this pathway to one of his nodes, and scratches his name into the back of the bus seat for fun. He scans around the bar before entering, taking in the environmental backcloth. He can see no sign of trouble, or cops ready to raid the bar, so he goes inside. The bar attracts many criminals, as it provides a safe place to do business. In this crime attractor, he converts the stolen credit cards to cash and heads home.

Summary

The continual development of GIS is the key to understanding the growth in thinking about space as a significant factor in the occurrence of crime. Indeed a positive feedback loop appears to be emerging, where advances in our understanding of criminal behaviour are driving the use of GIS in crime prevention. Concepts such as crime attractors and crime generators are valuable not only in the way that they can be mapped, but also in the way that they help practitioners conceptualise the underlying criminal behaviour. A map of crime is not the end point – it is a starting position on the way to understanding the real motivations and opportunities available to offenders and preventing criminal activity from happening.

Practical exercises

Cognitive map in practice

You receive information that John is stealing from cars. You work on this case with an operative policeman which gathers information on this case. You find out his house address and places that he frequents, those being his job place (he is working at a car wash), a casino and a bar.

Next we will determine his awareness space. In order to do that, you will determine the paths he is tacking in order to get to the points of interest.

The green buffer zone represents the space he knows best, the orange buffer is the exploration space and the red buffer represents a zone in which he is very unlikely to commit a crime, not feeling comfortable in that area because he doesn’t know it that well. Next we will be excluding the areas near his points of interest (house, job, casino and bar) because someone may recognize him in that area.

Next you can determine the attraction spots for John. In this case you will need to identify points of interest like parking spots.

Adding the crimes “stealing from cars” (black pushpin) with unknown author on your map will better show the crimes that intersects John’s awareness space, making John a suspect in these cases.

We received new information about John that he is leaving his home at 07:30 and reaches his job place at 08:00. We can filter the crimes on the map, taking in account time of crime, keeping only those that have been committed from 07:00 to 08:30 (when he is going to work) and 15:00 to 17:00 (when he is leaving from work) that have been committed during working days.

In the above case, the victim left his car at 07:35 in 12.09.2016. A crime is being committed when a victim’s cognitive map and the offender’s cognitive map intersect in space and time. So you have fulfilled 2 basic conditions for a crime to be committed, SPACE and TIME.

A third condition is GAIN. The victim has an expensive car with a good radio so the GAIN condition is also fulfilled. We know that John receives his salary on 15th of each month.

A forth condition is LOW RISK. The parking place is not guarded, so the forth condition is also fulfilled.

The last condition is OPORTUNITY. So we know that John passes through that parking spot, the time condition is also meet, the gain will be the expensive radio from the car and the parking place is not supervised. John always has at him a ceramic key which can break the window without making any noise. Nobody is around, so John now has the opportunity to commit the crime, if there is nothing making him uncomfortable, he will probably commit the crime.

Giving this information you can tell the officer working on the case to gather further information about John’s and focus on 12.09.2016 date.

The officer obtains new information about John, on that specific date, John was seen by his neighbours leaving the house at 07:30, and coming back at 08:00 and leaving very quickly. His boss told the police John was late, and came to work at 08:30. After checking at the casino, the manager reported that John came around 18:30 and stayed till late 22:00 having a big amount a money to spend, though we was constantly losing money.

All this information can lead us to believe that John committed that crime.

Manner of evaluation

For achieving the goals set for this training we recommend to have a series from 20 up to 25 students. The structure was calibrated on theoretical and practical applications on methods, techniques and tools (GIS software and add-ins). In fact, additionally to the manual, which can be used for individual study by the trainers and trainees, there were created power point presentations, practical exercises and the final, test which will take 2 hours in order to be solved.

The schedule is focused exclusively on a combination of the theoretical part with practical exercises.

In order to pass the final exam, you will need to obtain 60 % of points for each part of the test: theoretical and practical.

Example for final test:

Theoretical test

What is standard deviation?

A statistical measure of the spread of values from their mean, calculated as the square root of the sum of the squared deviations from the mean value, divided by the number of elements minus one

The accepted level of normal values, calculated according to previous data

A statistical measure used for calculating the mean value

What is spatial pattern analysis?

It’s the study of time and space

It’s the study of the spatial arrangements of points, lines or polygons in space

It’s the study of offenders

What is a mental map?

It’s a representation of the spatial environment which an individual carries in his mind

It’s a representation of the spatial environment which an offender carries out on a computer

It’s a representation of the spatial environment which police officers represent in ArcGIS

What is mean center?

The least centrally located point, line or polygon from the input feature class

It’s the average X and Y coordinate of all the features in the study area

The most centrally located feature in a point, line, or polygon input feature class

What is central feature?

The least centrally located point, line or polygon from the input feature class

It’s the average X and Y coordinate of all the features in the study area

The most centrally located feature in a point, line, or polygon input feature class

What is a hot spot?

An area that has a greater than average number of criminal or disorder events

It represents the areas with less than the average amount of crime or disorder

It represents the address where offenders live

What is the time span of an offence?

The duration within which the offender has been discovered

The duration within which the victim called for help

The duration within which the crime event happened

What is inverse distance weighting (IDW)?

It’s an interpolation technique used in a GIS application to create a smooth continuous surface when representing density of crimes

It’s a spatio-temporal tool that indicates when an offence has been committed

It’s a technique used for calculating the maximum distance between a set of points

What is environmental criminology?

It’s the study of criminal activity based on time factors

It’s the study of all the factors that contribute to criminal activities

It’s the study of criminal activity and victimization and how factors of space influence offenders and victims

Each question values: 1 pt.

By default: 1 pt.

Total: 10 pts.

Practical test

Copy the data from the given CD in Disk Drive D in a new folder you will create and name “FINAL EXAM DATA”. Open a “Blank Map” in ArcMap. Create connections to the new data (D:\FINAL EXAM DATA).

*Before starting, disconnect from all previous folder connections.

Using projected data from HRV_adm1.shp and points.shp, find out which county has the least points implemented. (write down the “Name 1”and “ID 1”fields of that county)

Using projected data from HRV_adm1.shp and points.shp, find out the number of points with “type” attribute “school” located in the county with the attribute “NAME_1” – “Grad Zagreb” has. Name the central feature of these points.

Using Zagreb_Offences_Proj_D2, find out how many assaults occurred on Friday during the night. Which weekday has the most offences committed?

Requirement 1: 3 pts.

Requirement 2: 3 pts.

Requirement 3: 3 pts.

By default: 1 pt.

Total: 10 pts.

SOLUTIONS

Theoretical test

A

B

A

B

C

A

C

A

C

Practical test

Bjelovarska-Bilogorska with id 1203

After adding the data to the map with project function in order to work with the correct coordinate system, use join function on administrative delimitation with the number of points. The result will be a new attribute called count, which represents the number of points that are placed in each administrative delimitation.

66 school points ; Centar za prakticnu robotiku (1215350969)

In order to solve this exercise, you will have to make a selection by attribute in order to have in one single set of data, all the points with the type attribute school. You will also need a selection on Grad Zagreb. After having these two set of data, make a select by location, in order to select all the schools in Grad Zagreb.

In order to obtain the central feature of these points, you will have to use central feature function.

18 ; Friday

Using frequency function, you can find out how frequent some occurrences are. In this case, you will want set frequency parameters for type of offence, weekday and day/night variation. As a result, you will get a table will the categories that have been earlier checked.

In order to find out which weekday is the most affected one by the total number of crimes, do the frequency function again, but this time just check the weekday category.

In order to pass the final exam, you will need to obtain 60 % of points for each part of the test: theoretical and practical.

The previous test is an example that can be used for further examinations.

Learning outcomes

Learn about patterns and standard deviation and how are they used in GIS; how are these functions integrated in software solutions; mathematical techniques that are used in pattern identification.

Everything about Hot spot (when, how, why and how to create a hotspot), Definition of Hotspot, why is it useful, how to use hotspot, how to create hotspot, how to understand a hotspot

Basic principal of temporal changes, observing temporal changes of offenders with the aim of documenting criminal activity, rules and concepts used, temporal notions regarding the offender or the crime.

Spatiality notions regarding the offender or the crime, aspects of criminal patterns taking into account the elements of spatiality

Enhancing the accumulated knowledge and evaluation of the trainees

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Annexes

DIGITAL DATA available on DVD:

GIS LVL 2 Data folder which contains:

Cogniteve map.gdb

croatia-latest.shp

GIS 1

HRV_adm

Zagreb_Offences_Proj_D2

FINAL EXAM DATA folder