Examining Application of Aggregated and Disaggregated Poisson–Gamma Models Subjected to Low Sample Mean Bias

Two general classes of models have been proposed for modeling crash data: disaggregated (both with and without time trend) and aggregated models. Poisson–gamma models have traditionally been used under both of these model classes. As documented in previous studies, data sets characterized by small sample size and low mean values can significantly affect the performance of Poisson–gamma models, particularly those related to the estimation of the inverse dispersion parameter. Thus, guidance is needed on when to use aggregated models instead of 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) could 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 this objective, several simulation runs were performed for different values describing the mean, the sample size, and the inverse dispersion parameter. The simulation scenarios represented cases where 3, 5, and 10 years of data were available. To help illustrate the proposed guidance, aggregated and disaggregated models were estimated with crash data collected from four-lane rural highways in Texas. This paper provides guidelines about which model classes are more reliable as a function of the sample mean values, the sample size, and the amount of dispersion observed in the raw data.