With a view towards reducing traffic accidents on roadways, various methods have been considered to predict accidents. In this study, we analyze traffic accident frequency models that employ fixed- and random-parameter negative binomial approaches. Random parameters enable the inclusion of unobserved heterogeneity in traffic accident data, which current popular methods with fixed parameters such as Poisson or negative binomial models cannot consider in terms of time variation or segment-specific effects. A continuous, unbalanced panel of accident histories for 208 four-way signalized intersections on national highways in Seoul was used to estimate a traffic accident occurrence model that considered traffic volumes and various geometric characteristics at intersections. The results revealed that the left-turn exclusive lanes and traffic volumes on minor roads had random parameters that affected the likelihood of accident frequencies differently; the other variables were found to significantly affect traffic safety at the intersections on the national highways as fixed parameters. Based on these results, it can be concluded that the same traffic safety facilities have different effects on traffic accidents on major and minor roads. The insights from this study suggest the need for a broader analysis of integrated guidelines for facilities that impact intersection accident propensities.