Examining the influence of link function misspecification in conventional regression models for developing crash...

Area of Science:

• Traffic safety engineering
• Statistical modeling
• Transportation research

Background:

• Crash Modification Factors (CMFs) are essential for evaluating the safety impact of road design and operational changes.
• Generalized Linear Models (GLMs) with linear link functions are commonly used for CMF development.
• Potential misspecification of link functions in regression models can affect CMF accuracy.

Purpose of the Study:

• To assess the accuracy of CMFs developed using standard regression models when variables exhibit nonlinear relationships.
• To quantify the bias introduced by nonlinear relationships and the degree of nonlinearity.
• To investigate the impact of link function misspecification on CMF development.

Main Methods:

• Utilized artificial realistic data to simulate crash counts based on assumed linear and nonlinear crash modification functions (CM-Functions).
• Derived CMFs using commonly employed GLMs with additive linear link functions under various scenarios.
• Compared derived CMFs against the true values from the simulated data.

Main Results:

• CMFs derived from standard GLMs are biased when variables have nonlinear relationships with crash risk, particularly at boundary conditions.
• Increased nonlinearity leads to more significant bias in the estimated CMFs.
• Misspecification of the link function can introduce bias in CMFs for both nonlinear and linear variables.

Conclusions:

• The choice of link function is critical for accurate CMF development using regression models.
• Standard GLMs may produce biased CMFs if underlying variable relationships are nonlinear.
• Careful consideration of functional forms and link functions is necessary to ensure reliable safety impact estimations.