The Crime Problem Management solution includes a custom geoprocessing tool in the Problem Identification project for ArcGIS Pro. This tool perform a statistical test used by crime analysts to evaluate whether evidence exists that a crime problem response resulted in a statistically significant reduction in crime.
Note:
The Weighted Displacement Difference (WWD) tool utilizes the Weighted Displacement Difference (WDD) statistical test. Wheeler, A.P., and Jerry H. Ratcliffe. 2018. "A Simple Weighted Displacement Difference Test to Evaluate Place Based Crime Interventions." Crime Science 7: 11. https://doi.org/10.1186/s40163-018-0085-5.
Understanding Weighted Displacement Difference
Weighted Displacement Difference is a statistical test (Wheeler and Ratcliffe 2018) intended to provide crime analysts and other law enforcement practitioners a straightforward method for determining the effectiveness of place-based responses to crime problems. The test compares the difference in incident counts between a problem response area's response period (treatment) and an equivalent period immediately preceding the response (pretreatment). These values are then compared with counts in a similarly sized control area. To determine whether incidents were reduced rather than displaced, the test also evaluates a displacement zone around each area. A negative test statistic indicates statistical evidence that the response reduced incidents, with lower values indicating stronger evidence of reduction. Additional guidance on this statistic is available in the original paper. To facilitate the use of this statistic in ArcGIS Pro, this project includes the Weighted Displacement Difference tool. This tool calculates the statistic based on your existing layers, helps you optimize choice control area, and creates a plain-language output message to simplify interpretation of the results.
Weighted Displacement Difference tool
The Weighted Displacement Difference Tool calculates weighted displacement difference statistics for incidents within a response area as compared with a control area. These statistics can be used to determine whether evidence exists that a policing response in a problem area reduced incidents during the treatment period when compared with a pretreatment period. To ensure that reductions are not due to displacement of incidents, the statistic accounts for a displacement area around both the response area and the control area.
Usage
- The output feature class will create a polygon for the following five features:
- Response Area—A feature defined by the Input Response Area parameter feature that includes incident count information from the Input Incident Features parameter features.
- Control Area—A feature defined by the Input Control Area parameter feature that includes incident count information from the Input Incident Features parameter features.
- Response Displacement Area—A feature generated by creating a buffer around the response area at the distance specified in the Displacement Distance parameter.
- Weighted Displacement Difference Results—A multipart feature that contains the response area and response displacement area part, the control area control displacement area part, and the calculated statistics.
- The following fields will be added to the output:
- AREATYPE—The identifying name given to the feature. This value will be Response Area, Control Area, Response Displacement Area, Control Displacement Area, or Weighted Displacement Difference Results.
- PREV_CNT—The number of points found within the feature area during the pretreatment period. This value is null for the feature labeled Weighted Displacement Difference Results in the Area Type field.
- RESP_CNT—The number of points found within the feature area during the treatment period. This value is null for the Weighted Displacement Difference Results feature.
- DIFF_CNT—The difference between the RESP_CNT and PREV_CNT fields. This value is null for the Weighted Displacement Difference Results feature.
- PERC—The percentage of change between the RESP_CNT and PREV_CNT fields. This value is null for the Weighted Displacement Difference Results feature.
- SEWDD—The standard error value of the weighted displacement difference. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- ZWDD—The z-score value of the weighted displacement difference. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- ONETPV—The one tailed p-value of the weighted displacement different. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- CONFITVLLO—The lower limit of the 95% confidence interval. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- CONFITVLHI—The upper limit of the 95% confidence interval. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- RESPSTART—The start date of the treatment period. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- RESPEND—The end date of the treatment period. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- PREVSTART—The start date of the pretreatment period. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- PREVEND—The end date of the pretreatment period. This value is null for the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
- The Input Incident Features parameter layer should include a rolling three years' worth of historical data. This historical data is used to assess suitability of a control area by comparing a three-year linear trend.
- Records from Input Incident Features with a null or empty Incident Date Field value will be ignored as part of the calculation.
- The treatment period is the number of days from the Response Start Date Field value through the Response End Date Field value. The pretreatment period is determined automatically by counting backward from the day before the response start date for the same number of days as the treatment period.
- The tool generates a summary message in the tool dialog box that describes the suitability of the control area relative to the threshold values specified by the Maximum Area Size Difference (%), Maximum Pre-treatment Count Difference (%), Minimum Absolute Correlation Coeffecient parameters. If any threshold is not met, the tool fails and displays an error message that identifies the unmet threshold values. If all three thresholds are met, the tool will completes and displays the actual differences for all three metrics. The threshold requirements for each test are as follows:
- Maximum Area Size Difference (%)—If actual absolute percent difference exceeds this threshold then, the control area is not suitable for use in the weighted displacement difference statistic, and an error appears in the tool dialog box.
- Maximum pretreatment Count Difference (%)—If the actual absolute percent difference exceeds this threshold, the control area is not suitable for use in the weighted displacement difference statistic, and an error appears in the tool dialog box.
- Minimum Absolute Correlation Coeffecient—If the actual absolute correlation coefficient exceeds this threshold, the control area is not suitable for use in the weighted displacement difference statistic, and an error appears in the tool dialog box.
- The tool generates a summary message in the tool dialog box describing the statistical findings. This summary includes a text-based characterization proposed by Wheeler and Ratcliffe that describes the strength of the statistical evidence derived from the analysis. This text-based characterization can be used to communicate analytical results. The characterization corresponds directly to the Weighted Displacement Difference Z-score value:
- No evidence of reduction: ZWDD > -1.3. This does not mean there is no evidence, especially if z is below 0, just that the evidence is significant enough to not have happened by chance.
- Weak evidence of reduction: -1.6 < ZWDD ≤ -1.3
- Moderate evidence of reduction: -2.3 < ZWDD ≤ -1.6
- Strong evidence of reduction: -3.1 < ZWDD ≤ -2.3
- Very strong evidence of reduction: ZWDD ≤ -3.1
- Tool output messages can be copied to the clipboard for pasting into attribute fields of the CrimeProblemResponses layer to document the results of the statistical evaluation. Copying the output message using Ctrl + C removes HTML formatting tags, while right-clicking and selecting Copy All preserves HTML formatting tags.
Syntax
WeightedDisplacementDifference (in_response_feature, {where_clause}, in_control_feature, in_features, out_features, start_date_field, end_date_field, incident_date_field, displacement_distance, {test_suitability}, {max_area_difference}, {max_count_difference}, {min_correlation_coefficient})
| Parameter | Explanation | Data type |
|---|---|---|
Input Response Area in_response_feature | The input polygon feature layer containing a problem response area polygon feature for which the weighted displacement statistic will be calculated. | Feature Layer |
Expression (Optional) where_clause | The SQL expression used to select a subset of the input datasets' records. If multiple input datasets are specified, they will all be evaluated using the expression. If no records match the expression for an input dataset, no records from that dataset will be appended to the target. For more information about SQL syntax, see SQL reference for query expressions used in ArcGIS. | SQL Expression |
| Input Control Area in_control_feature | The input feature layer containing a polygon control area feature. This feature can be from an existing feature layer or created using the draw tool. The feature is used to compare incident counts in both treatment periods against the response area as part of the weighted displacement difference statistic. | Feature Set |
| Input Incident Features in_features | The input point feature layer containing crime or calls for service incidents for which counts will be generated in response, control, and displacement areas for treatment and pretreatment periods. | Feature Layer |
| Output Feature Class out_features | Output polygon feature class containing weighted displacement difference results. | Feature Class |
| Response Start Date Field start_date_field | The field in the Input Response Area layer that contains the date on which the response treatment started. | Field |
| Response End Date Field end_date_field | The field in the Input Response Area layer that contains the date on which the response treatment ended. | Field |
| Incident Date Field incident_date_field | The field in the Input Incident Features layer that contains the date on which the incident occurred. | Field |
| Displacement Distance displacement_distance | The distance around the input response area and input control area that will be buffered. Buffered area will be used in the statistic to test for evidence of incident displacement. | Linear Unit |
| Test Control Area Suitability test_suitability | Specifies whether theMaximum Area Size Difference (%), Maximum Pre-treatment Count Different (%), and Minimum Absolute Correlation Coefficient threshold checks will be performed to assess the suitability of the control area relative to the response area for use in the weighted displacement difference statistic. For accuracy, the control area should be similar to the response area. | Boolean |
| Maximum Area Size Difference (%) max_area_difference | The maximum threshold for absolute percent difference in size between the response area and control area. This parameter is enabled only when the test_suitability parameter is set to TEST. The default value is 20%. | Double |
| Maximum Pre-treatment Count Difference (%) max_count_difference |
The maximum threshold for absolute percent difference in incident counts during the pretreatment period between the response area and control area. This parameter is enabled only when the test_suitability parameter is set to TEST. The default value is 20%. | Double |
| Minimum Absolute Correlation Coeffecient min_correlation_coefficient | The minimum threshold for absolute correlation coefficient for a rolling three-year period between the response area and control area. The correlation coefficient is calculated using Pearson's R and measures the linear trend between both areas for a rolling three-year period starting on the day before the Response Start Date Field. This parameter is enabled only when the test_suitability parameter is set to TEST. The default value is 0.7. | Double |
Licensing information
- Creator: Yes
- Professional: Yes
- Professional Plus: Yes
References
Wheeler, A.P., and Jerry H. Ratcliffe. 2018. "A Simple Weighted Displacement Difference Test to Evaluate Place Based Crime Interventions." Crime Science 7: 11. https://doi.org/10.1186/s40163-018-0085-5.