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Weighted Displacement Difference Tool Reference

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  1. Understanding Weighted Displacement Difference

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., Ratcliffe, J.H. A simple weighted displacement difference test to evaluate place based crime interventions. Crime Sci 7, 11 (2018). https://doi.org/10.1186/s40163-018-0085-5

Understanding Weighted Displacement Difference

Weighted Displacement Difference is a statistical test (Wheeler, A.P., Ratcliff, J.H.) intended to provide crime analysts or other law enforcement practitioners a straightforward method for determining effectiveness of place-based responses to crime problems. The test compares incident count differences for a problem response area from the response period (treatment) to an equivalent length period immediately preceding the response (pre-treatment). These values are then compared to counts in a similarly-sized control area, and to ensure that incidents are actually reduced rather than displaced, a displacement zone around each area is also evaluated. A negative test statistic value indicates statistical evidence for the reduction of incidents due to the response, with lower test statistic values representing stronger evidence of reduction. Additional guidance on this statistic can be found in the original paper. To help 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 tool results.

Weighted Displacement Difference tool

Calculates weighted displacement difference statistics for incidents within a response area as compared to a control area. These statistics can be used to determine if evidence exists that a policing response in a problem area reduced incidents during the treatment period when compared to a pre-treatment 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 including incident count information from the Input Incident Features parameter features.
    • Control Area - A feature defined by the Input Control Area parameter feature including 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 multi-part feature containing the response area and response displacement area part, and the control area control displacement area part; as well as 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 pre-treatment 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 in 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 in 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 in 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 in 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 in 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 in 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 in the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
    • PREVSTART - The start date of the pre-treatment period. This value is null for in the output of the Response Area, Control Area, Response Displacement Area, and Control Displacement Area features.
    • PREVEND - The end date of the pre-treatment period. This value is null for in 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 determined as the number of days between the Response Start Date Field and Response End Date Field parameters. The pre-treatment period is automatically determined, starting at the day before the value entered in the Response Start Date Field, and going backwards the same number of days as the number of days in the treatment period.
  • The tool generates a summary message in the tool dialog box describing the suitability of the control area relative to the threshold values specified in Maximum Area Size Difference (%), Maximum Pre-treatment Count Difference (%), Minimum Absolute Correlation Coeffecient parameters. If any of the thresholds are not met, the tool will fail, and an error message will be displayed with information about which threshold values were not met. If all three thresholds are met, the tool will successfully complete and display the actual differences across all three-threshold metrics. The threshold requirements for each test:
    • 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 will be displayed in the tool dialog box.
    • Maximum Pre-treatment Count 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 will be displayed in the tool dialog box.
    • Minimum Absolute Correlation Coeffecient - If actual absolute correlation coefficient exceeds this threshold then, the control area is not suitable for use in the weighted displacement difference statistic, and an error will be displayed 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: Zwdd <=-1.3 and >-1.6
    • Moderate evidence of reduction: Zwdd <=-1.6 and >-2.3
    • Strong evidence of reduction: Zwdd <=-2.3 and >-3.1
    • 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 ExplanationData 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 pre-treatment 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 statistic to test for evidence of incident displacement.

Linear Unit

Test Control Area Suitability

test_suitability

Specifies whether to perform Maximum Area Size Difference (%), Maximum Pre-treatment Count Different (%), and Minimum Absolute Correlation Coefficient threshold checks to assess the suitability of the control area for use in the weighted displacement difference statistic as compared to the response area.

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 pre-treatment 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. Correlation coefficient is calculated using Pearson's R and measures the linear trend between both areas for a rolling three-year period starting at 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:

  • ArcGIS Desktop Basic: Yes
  • ArcGIS Desktop Standard: Yes
  • ArcGIS Advanced: Yes

Reference:

Wheeler, A.P., Ratcliffe, J.H. A simple weighted displacement difference test to evaluate place based crime interventions. Crime Sci 7, 11 (2018). https://doi.org/10.1186/s40163-018-0085-5

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In this topic
  1. Understanding Weighted Displacement Difference