Insights into plausible methodological frameworks specifically with respect to two key issues - (1) mathematical formulation of the underlying process affecting median crossover accidents and (2) the factors affecting median crossover frequencies in Washington State - are provided in this study. Random effects negative binomial (RENB) and the cross-sectional negative binomial (NB) models are examined. The specification comparisons indicate benefits from using the RENB model only when spatial and temporal effects are totally unobserved. When spatial and temporal effects are explicitly included, the NB model is statistically adequate, while the RENB model appears to lose its distributional advantage. Such findings might be artifacts of the median crossover accident dataset used in this study. While the NB model appears to be the superior model in the present case of median crossover accidents, the marginally inferior performance of the RENB model warrants further examination through application to regular accident types in light of its flexibility to incorporate temporal and cross-sectional variations simultaneously in panel counts. From a predictive standpoint, RENB offers advantages in terms of model transferability and updating.