Effects of Sample Size on Goodness-of-Fit Statistic and Confidence Intervals of Crash Prediction Models Subjected to Low Sample Mean Values

Abstract

The statistical relationship between motor vehicle crashes and covariates can generally be modeled via generalized linear models (GLMs) with logarithmic links with errors distributed in a Poisson or Poisson-gamma manner. The scaled deviance and Pearson's χ2 have been proposed to test the statistical fit of GLMs. Recent studies have shown that these two estimators are not adequate for testing the goodness of fit (GOF) of GLMs when they are developed from data characterized by low sample mean values. To circumvent this problem, a testing method has been proposed to evaluate the GOF of such GLMs. Because this method can be time-consuming to implement, there is a need to determine whether it is sensitive to different sample sizes. The primary objective of this paper is to investigate the effects of decreasing sample sizes on the GOF testing technique. A secondary objective is to estimate how the reducing of sample size influences the confidence intervals of GLMs. To accomplish the objectives, GLMs were fit wi...