The Predictive Analysis application facilitates creating, managing, evaluating, and updating your agency’s Safety Performance Functions (SPFs) for both segments and intersections in an easily accessible interface. Agencies that have not yet developed SPFs can use Predictive Analysis to generate unique SPFs for their roadways based on the Optimal Fit function. Agencies with previously developed SPFs can use Predictive Analysis to evaluate the performance of their SPFs for each segment sub-type, and make any modifications as needed to improve their performance. Additionally, all agencies can use Predictive Analysis to keep a running history of their SPFs and track how they have changed over time.

The Segment Selector dropdown of Predictive Analysis allows users to search for and select which segment type they would like to evaluate. All segments are grouped according to the unique characteristics determined by your organization. For example, it’s common to group segments by Interstate/Non-Interstate, Urban/Rural, and the number of lanes. Users can select the segment characteristics from the dropdown to display that segment type, and the results will be displayed in the SPF preview.

The Segment Selector is used to choose segment characteristics.

Once the user has selected the Segment Grouping to evaluate, the SPF preview will display the actual Safety Performance Function, and the date on which it was last modified. Administrators will also have the ability to edit the Function and view the history of the SPF. This can be used to evaluate the effectiveness of any updates or changes to the Function.

The SPF Preview window displaying the results.

If no Function is currently defined, administrators can click the Edit Function button to set the Function to the Optimal Fit, which is Numetric’s recommended SPF for that Segment Grouping (for more detail on the Optimal Fit feature, see the Optimal Fit section of this article). Alternatively, administrators can edit the Function to enter their own SPF for that Segment Grouping.

The SPF Preview with no Function displayed.

When a Segment Grouping with an operational Function is selected, users can see a graph that plots each segment that meets the grouping criteria. Each segment is plotted with the number of Crashes Per Mile on the vertical axis, and the AADT on the horizontal axis. Each point on the graph represents a Segment. The Blue line represents the SPF, as it is currently defined, and the CURE, and ±2 Sigma are indicated by dotted and dashed lines respectively. Additionally, the R-squared value is provided to help users understand the distribution of the segments.

The SPF Preview graph with the SPF, CURE, ±2 Sigma and R-squared values displayed.

The CURE, or Cumulative Residual, is calculated by adding the difference between the number of crashes projected by the SPF, and the number of crashes actually occurring for each AADT.

The +/- 2 Sigma is a representation of plus, or minus 2 standard deviations.

The Details Sidebar displays metrics related to the selected Segment Grouping: % of Roadway, % of Crashes, # of segments, and # of Segments with AADT.

The % of Roadway metric indicates the percentage of the total statewide roadway that is represented in this Segment Grouping. In the example below, 4.93% of the total statewide roadway system is represented by this Segment Grouping.

The % of Crashes metric indicates the percentage of the total number of statewide crashes represented in this Segment Grouping. In the example below, 5.10% of the number of statewide crashes are represented by this Segment Grouping.

The # of Segments metric indicates the number of segments contained in this Segment Grouping. In the example below, there are 40,469 segments contained in this Segment Grouping.

The # of Segments with AADT metric indicates the number of segments contained in this Segment Grouping for which we have AADT data available. In the example below, there are 40,469 segments in this Segment Grouping for which we have AADT available.

The Detail Sidebar with the % of roadway, % of crashes, # of segments, and # of Segments with AADT metrics displayed.

The Details to This allows agencies to track the performance of their SPFs over time, and track historical changes to the function.

Predictive Analysis also allows users to track and view the history of their SPFs. The Edit History & Comments section of the Details Sidebar displays the history of the actual SFP, and any comments that have been added. In this example, we can see that the Optimal Fit feature was used to define the SPF for this Segment Grouping on the Nov. 20, 2024.

The Details Sidebar displaying the current SPF, when it was defined, and who defined it.

Clicking on any of the points in the SPF Preview chart will highlight that segment in the chart, and open a flyout for the selected segment. This Segment Flyout contains the roadway details, and summary of the selected segment, as well as a Google Streetview thumbnail for the segment.

Additionally, the selected segment (point) will display the Expected Crashes per mile based Empirical Bayes calculations. Additionally, the Adjusted Performance Expectations section in the Segment Flyout will display the expected crashes per mile, and expected crash rate, also based on Empirical Bayes calculations.

The flyout for a selected Segment.

Administrators can also use Predictive Analysis to edit and revise individual Functions. These edits are tracked and allow for historical analysis, making it easy to see if the revisions to the Function are having the desired outcome.

The Edit Function window for the selected function.
​

The Predictive Analysis application provides its users with an optimal fit functionality, which can be used to generate an SPF based on Numetric’s Optimal Fit feature, which minimizes the average error between the annual crash rates for each of the segments and the SPF.

If an SPF is not entered for the selected Segment Grouping, a button will display the option to Set to Optimal Fit. By clicking on this, administrators can set Numetrics Optimal Fit as the Function for that Segment Grouping.

The Set to Optimal Fit button in the Function Preview window of a given Segment Grouping.

The Intersection Selector section of Predictive Analysis allows users to search for and select which Intersection type they would like to evaluate. Intersections are grouped according to the parameters set by your organization. For example, intersections can be grouped by the number of legs, the intersection control type, and crash attributes. Users can select the intersection characteristics from the dropdown to display all intersections of that type.

The Intersection selector dropdown options.

Once the user has selected the Intersection Grouping to evaluate, the SPF preview will display the actual Safety Performance Function, and the date on which it was last modified. Administrators will also have the ability to edit the Function and view the history of the SPF. This can be used to evaluate the effectiveness of any updates or changes to the Function.

If no Function is currently defined, administrators will be prompted to set the Function to the Optimal Fit, which is Numetric’s recommended SPF for that Intersection Grouping (for more detail on the Optimal Fit feature, see the Optimal Fit section of this article). Alternatively, administrators can edit the Function to enter their own SPF for the selected intersection.

(The SPF Preview with no Function displayed.)

When an Intersection Grouping with an operational Function is selected, users can see a 3-axis graph that plots each individual intersection that meets the grouping criteria. The X axis of the graph represents AADT of the intersection leg with a greater AADT, the Y axis of the graph represents the AADT of the intersection leg with a smaller AADT, and the Z axis represents the number of crashes. Users can click and drag to rotate the chart.

(The Intersection Graph with the XYZ flyout for a specific intersection displayed.)

The Details Sidebar displays metrics related to the selected Intersection Type: % of Roadway, % of Crashes, # of Intersections, and # of Intersections with AADT.

The % of Roadway metric indicates the percentage of the total statewide roadway that is represented in this Intersection Grouping. In the example below, 0.16% of the total statewide roadway system is represented by this Intersection Grouping.

The % of Crashes metric indicates the percentage of the total number of statewide crashes represented in this Intersection Grouping. In the example below, 1.37% of the number of statewide crashes are represented by this Intersection Grouping.

The # of Intersections metric indicates the number of intersections contained in this Intersection Grouping. In the example below, there are 420 intersections contained in this Intersection Grouping.

The # of Intersections with AADT metric indicates the number of Intersections contained in this Intersection Grouping for which we have AADT data available. In the example below, there are 419 Intersections in this Intersection Grouping for which we have AADT available.

The Detail Sidebar with the % of roadway, % of crashes, # of Intersections, and # of Intersections with AADT metrics displayed.

The Details to This allows agencies to track the performance of their SPFs over time, and track historical changes to the function.

Predictive Analysis also allows users to track and view the history of their SPFs. The Edit History & Comments section of the Details Sidebar displays the history of the actual SFP, and any comments that have been added. In this example, we can see that the Optimal Fit feature was used to define the SPF for this Intersection Grouping on May 15, 2024.

Clicking on any of the points in the SPF Preview chart will highlight that intersection in the chart, and open a flyout for the selected intersection. This Intersection Flyout contains the intersection details, and summary of the selected intersection, as well as a Google Streetview thumbnail for the intersection.

Additionally, the selected intersection (point) will display the Expected Crashes per mile based Empirical Bayes calculations. Additionally, the Adjusted Performance Expectations section in the Intersection Flyout will display the expected crashes per mile, and expected crash rate, also based on Empirical Bayes calculations.

The flyout for a selected Intersection.

Administrators can also use Predictive Analysis to edit and revise individual Functions. These edits are tracked and allow for historical analysis - making it easy to see if the revisions to the Function are having the desired outcome.

The Edit Function window, with the user modifying a portion of the selected function.

The Predictive Analysis Intersections application provides its users with an optimal fit functionality, which can be used to generate an SPF based on Numetric’s Optimal Fit feature, which minimizes the average error between the annual crash rates for each of the Intersections and the SPF.

If an SPF is not entered for the selected Intersection Grouping, a button will display the option to Set to Optimal Fit. By clicking on this, administrators can set Numetrics Optimal Fit as the Function for that Intersection Grouping.

(The Set to Optimal Fit button in the Function Preview window of a given Intersection Grouping.)