Trb06-0960 Effects of Sample Size on the Goodness-of-fit Statistic and Confidence Intervals of Crash Prediction Models Subjected to Low Sample Mean Values

The statistical relationship between motor vehicle crashes and covariates can generally be modeled via generalized linear models (GLMs) using logarithmic links with errors distributed in a Poisson or Poisson-gamma manner. The scaled deviance (SD) and Pearson’s X are tools that have been proposed to test statistical fit of GLMs. Recent studies have shown that these two estimators are not adequate for testing the goodnessof-fit (GOF) of GLMs when they are developed from data characterized with low sample mean values. To circumvent this problem, a testing method has been proposed to evaluate the goodness-of-fit of such GLMs. Given the fact that this method can be timeconsuming to implement, there is a need to determine whether this technique is sensitive to different sample sizes. The primary objective of this paper was to investigate the effects of decreasing sample sizes on the GOF testing technique. A secondary objective was to estimate how the reducing of sample size influences the confidence intervals of GLMs. In order to accomplish the objectives of the study, GLMs were fitted using two datasets subjected to average and low sample means collected in Toronto, Ontario. Several models were estimated for different sample sizes. The results of the study show that the testing technique is more effective for smaller samples than for larger samples when data is subjected to low sample mean values. The results also show that the width of the confidence intervals increases, as expected, as the sample size decreases, and can be extremely large for very small sample sizes. Hence, statistical models characterized by low sample mean values should be developed using a large number of observations. In fact, it is recommended to develop models using datasets containing at least 100 observations (e.g., intersections, segments, etc.). The paper concludes with recommendations for future studies involving such datasets.