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Mapping the Risk Terrain for Crime Using Machine Learning

Abstract

Objectives

We illustrate how a machine learning algorithm, Random Forests, can provide accurate long-term predictions of crime at micro places relative to other popular techniques. We also show how recent advances in model summaries can help to open the ‘black box’ of Random Forests, considerably improving their interpretability.

Methods

We generate long-term crime forecasts for robberies in Dallas at 200 by 200 feet grid cells that allow spatially varying associations of crime generators and demographic factors across the study area. We then show how using interpretable model summaries facilitate understanding the model’s inner workings.

Results

We find that Random Forests greatly outperform Risk Terrain Models and Kernel Density Estimation in terms of forecasting future crimes using different measures of predictive accuracy, but only slightly outperform using prior counts of crime. We find different factors that predict crime are highly non-linear and vary over space.

Conclusions

We show how using black-box machine learning models can provide accurate micro placed based crime predictions, but still be interpreted in a manner that fosters understanding of why a place is predicted to be risky.

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Fig. 1
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Data Availability

Data and code to replicate the results can be downloaded from https://www.dropbox.com/sh/b3n9a6z5xw14rd6/AAAjqnoMVKjzNQnWP9eu7M1ra?dl=0.

Notes

  1. 1.

    For more discussion about self-exciting point processes, see the full issue of Statistical Science volume 33(3) with several commentaries on Reinhart (2018) as well as a rejoinder responding to these commentaries.

  2. 2.

    Why a grid cell is estimated to be high risk should not imply that the highlighted covariates are then a causal explanation for crime. The identified land use features correlate with crime and hopefully predict better than chance where future crime will occur, but one should not infer a causal mechanism.

  3. 3.

    Even these are not exclusive of how one may measure the impact of a crime generator. Another common approach is to estimate the number of generators nearby, where nearby is either a specific buffer distance, or determined via adjacency of some aggregate unit (Bernasco and Block 2011; Haberman and Ratcliffe 2015; Murray and Roncek 2008; Wheeler 2019b).

  4. 4.

    See the related discussion on how encoding of the interactions in Deryol et al. (2016) was innapropriate to actually estimate interaction effects (Reinhart 2016).

  5. 5.

    Thus a clear difference of predictive models as compared to explanatory models is that the goal is to predict (out-of-sample) crime. That is, the main goal is not to derive causal hypotheses from a causal theoretical model and test these using empirical data. Instead, the goal of predictive models is to predict new or future observations (e.g. point estimates, interval predictions, or rankings).

  6. 6.

    The most accurate forecasting models are often models that combine different machine learning methods that together predict crime. Using the same logic, our paper is not antagonistic of self-exciting point process models (Mohler et al. 2011). Instead, we see the value of using such methods to predict short-to-medium crime occurrence, while our models can be used to predict medium-to-long term crime trends and also allow for crime predictions in ‘what-if’ scenarios.

  7. 7.

    Given these crime generator variables come from various sources, they are not uniformly prior to the crime counts used in the research. While the street index database is based on 2014 data, many of the other factors are based on more recent data collections. We do not believe it represents a large threat to the findings though, as many of the factors are historically stable due to long standing zoning laws in Dallas (Fischel 2015).

  8. 8.

    Given the large size of the variable set, we do not test for half block increments of 200 feet. Caplan et al. (2013a, b) suggest to limit the variable count to 100 or less.

  9. 9.

    Simpson’s Index for a block group equals \(\left( {p_{\text{white}} } \right)^{2} + \left( {p_{\text{black}} } \right)^{2} + \left( {p_{\text{Hispanic}} } \right)^{2}\) where p represents the proportion of that particular racial group.

  10. 10.

    The fixed L2 costs are one aspect we are not able to replicate given public descriptions. We considered two L2 costs of 1 and 5 in this step. To determine the best L1 penalty we use cross-validation, consistent with the code provided in Kennedy et al. (2016).

  11. 11.

    We conduct RTM analysis that both excludes demographic factors as well includes demographic factors. The models that included demographic factors were much more accurate than those that did not along all of the metrics we evaluate, so we only report the RTM model that includes demographic factors into the model selection process. “Appendix 2” lists the final produced RTM model.

  12. 12.

    The default settings in the ranger implementation are used, i.e. the number of trees is set to 500, and resampling is done with replacement.

  13. 13.

    Several of the sawtooth or flat line patterns are due to how we treat prediction ties in Fig. 1, most noticeable for the plot in the top right and the plot in the bottom left. Here we present the worst case scenario, sorting the predictions in descending order, and the future crimes in ascending order. This is typically how ROC plots are displayed (Davis and Goadrich 2006), and so it is similarly appropriate for these metrics as well.

  14. 14.

    To calculate the expected number of crimes per the kernel density estimate we multiplied the intensity kernel density value by the area of the grid cell, thus getting an expected number of crimes per grid cell.

  15. 15.

    Because of the size of the dataset and number of variables, to calculate this we selected a stratified sample of 2000 cases within 10 strata (so overall 20,000 cases). The strata were defined by the crime counts in the cells, with ties broken by the predicted number of crimes.

  16. 16.

    The correct predictive interpretation of a regression coefficient is a comparison between grid cells: how much does crime differ, on average, when comparing two groups of grid cells that differ by 1 in the relevant predictor while being identical in all the other predictors. Only under stringent assumptions can one make a counterfactual interpretation of changes within grid cells: the expected change in crime in that grid cell caused by adding 1 to the relevant predictor, while leaving all the other predictors in the model unchanged (see Gelman and Hill 2006, p. 34). With perhaps a few exceptions, all studies cited in this paper are of the former type.

  17. 17.

    Such average predictive comparisons can be used to understand any complicated regression model, not just random forests, see Gelman and Pardoe (2007) for a similar procedure. It is also very similar in nature to the local derivatives reported in Hipp et al. (2017).

  18. 18.

    An additional way to examine interactions are via Friedman’s H statistic (Friedman and Popescu 2008; Wang et al. 2016).

  19. 19.

    For example, a location may have a predicted 5 crimes in the area: the distance to the nearest liquor store contributes 3.6 to that prediction, while the proportion in poverty contributes 1.3, and the rest of the predictor variables combine for the additional 0.1 predicted crimes (including factors that potentially decrease crime).

  20. 20.

    We have provided supplementary random forest models to illustrate this confounding in “Appendix 3”. One is a model only using the exact same variables as the RTM model (the binary indicators and the demographic factors), and another using only the XY coordinates of the grid cell. While the model presented in the paper outperforms either, random forests trained on those different subsets of data still provide excellent future predictions.

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Appendices

Appendix 1: Crime Generator Data Source and SIC Code Classifications

This appendix provides additional information on the source of the crime generator data, as well as the SIC codes associated with different business categories. Store Front Index point data for Dallas can be downloaded from https://github.com/dillonma/storefrontindex. Public data downloads are mostly taken from https://gis.dallascityhall.com/shapefileDownload.aspx or http://gis.dallascityhall.com/wwwgis/rest/services. Texas schools are taken from https://schoolsdata2-tea-texas.opendata.arcgis.com/. The only reason check cashing stores are taken from Reference USA as opposed to Lexis Nexis is my local library cut the service for Lexis Nexis. The storefront data are businesses as of 2015. The rest of datasets were collected in 2018.

See Tables 4 and 5.

Table 4 Crime generator data sources
Table 5 SIC codes associated with different business categories

Appendix 2: RTM Predicted Model

See Table 6.

Table 6 The final selected model produced by risk terrain modelling, negative binomial model

Appendix 3: Additional Random Forest Model Performance Metrics

See Fig. 5.

Fig. 5
figure5

Predictive statistics for supplementary random forest models. “RF: Full Model” is the same model as that presented in the main manuscript for Random Forests, and “RTM” is the original RTM model in the main manuscript. “RF: only XY” is a random forest model trained with only the XY coordinates. “RF: RTM variables” is a random forest model trained with the exact same variables input into RTM (dummy variables for distance and density, plus continuous variables for demographic characteristics)

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Wheeler, A.P., Steenbeek, W. Mapping the Risk Terrain for Crime Using Machine Learning. J Quant Criminol 37, 445–480 (2021). https://doi.org/10.1007/s10940-020-09457-7

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Keywords

  • Risk-terrain-models
  • Micro-places
  • Machine-learning
  • Random forests
  • Robbery