Out-of-sample prediction and interpretation for random parameter generalized linear models.

Area of Science:

• Statistics
• Econometrics
• Transportation Engineering

Background:

• Generalized linear models (GLMs) with random parameters (RPs) enhance model fit and address unobserved heterogeneity.
• Predicting outcomes for new observations using RP-GLMs is challenging, with existing methods often yielding biased or computationally intensive results.

Purpose of the Study:

• To develop a statistically rigorous and computationally efficient method for out-of-sample predictions in RP-GLMs.
• To provide accurate prediction variance estimation for out-of-sample observations.
• To derive closed-form equations for elasticities and marginal effects of RPs.

Main Methods:

• Leveraging fundamental statistical theory and properties of RP distributions (normal, lognormal, triangular, uniform, gamma) within a log-link GLM framework.
• Developing an exact prediction method and closed-form equations for elasticities and marginal effects.
• Testing the proposed method using crash frequency prediction models from the Highway Safety Information System (HSIS).

Main Results:

• The proposed exact method yields more accurate out-of-sample predictions compared to simulation-based approximations.
• The method provides direct and accurate estimation of prediction variance for out-of-sample observations.
• The approach is computationally simple and suitable for practical applications.

Conclusions:

• The developed exact method offers a superior alternative for out-of-sample predictions in RP-GLMs.
• This methodology facilitates the broader application of RPs in statistical modeling and research.
• The findings are particularly relevant for transportation safety analysis and other fields utilizing GLMs.