Goodness-of-fit testing for accident models with low means

The modeling of relationships between motor vehicle crashes and underlying factors has been investigated for more than three decades. Recently, many highway safety studies have documented the use of negative binomial (NB) regression models. On rare occasions, the Poisson model may be the only alternative especially when crash sample mean is low. Pearson's X(2) and the scaled deviance (G(2)) are two common test statistics that have been proposed as measures of goodness-of-fit (GOF) for Poisson or NB models. Unfortunately, transportation safety analysts often deal with crash data that are characterized by low sample mean values. Under such conditions, the traditional test statistics may not perform very well. This study has three objectives. The first objective is to examine all the traditional test statistics and compare their performance for the GOF of accident models subjected to low sample means. Secondly, this study proposes a new test statistic that is not dependent on the sample size for Poisson regression model, as opposed to the grouped G(2) method. The proposed method is easy to use and does not require grouping data, which is time consuming and may not be feasible to use if the sample size is small. Moreover, the proposed method can be used for lower sample means than documented in previous studies. Thirdly, this study provides guidance on how and when to use appropriate test statistics for both Poisson and negative binomial (NB) regression models.