Examining the Application of Aggregated and Disaggregated Poisson-Gamma Models Subjected to Low Sample Mean Bias.

The costs of collecting crash and other related data can be very prohibitive. As a result, these data can often only be collected at a limited number of sites. One way to increase the sample size for developing reliable statistical models is to collect data at the same sites for a long time period. Two general classes of models have been proposed for modeling crash data using such datasets: disaggregated (with and without time-trend) and aggregated models. Poisson-gamma models have traditionally been used under these two model classes. As documented in previous studies, datasets characterized by small sample size and low mean values can significantly affectthe performance of Poisson-gamma models, particularly the one related to the estimation of the inverse dispersion parameter. Thus, there is a need to provide guidance about when aggregated models should be used over disaggregated models as a function of the sample size and the sample mean value. The objective of this study was to estimate the conditions in which aggregated models (with a higher mean, but a smaller sample size) provide a more reliable estimate of the inverse dispersion parameter than disaggregated models (with a lower sample mean value, but a larger sample size) or vice versa. To accomplish the objective of this study, several simulation runs were performed for different values describing the mean, the sample sizeand the inverse dispersion parameter. The simulation scenarios represented cases where 3, 5 and 10 years of data are available. To help illustrate the proposed guidance, aggregated and disaggregated models were estimated using crash data collected on 4-lane rural highways in Texas. The results of the study show that the selection of the model class is influenced by the sample mean values, the sample size and the amount of dispersion observed in the raw data. Overall, for sample mean values equal to 0.5 crashes per year (for the entire study period), aggregated models are favored over disaggregated models, especially when the inverse dispersion parameter is above 1.0. When the sample mean is at least equal to one, disaggregated models provide more reliable estimates than aggregated models.