A multiple membership multilevel negative binomial model for intersection crash analysis

Many intersections belong to more than one zone, but most research has not considered the effects of multiple zones in intersection crash analysis. This issue is known as a boundary problem. Unobserved heterogeneity between zones can lead to model misspecification which can result in biased parameter estimates and poor model fitting performance. This study investigated the issue using five years of intersection crash data from the City of Regina, Saskatchewan, Canada. The study developed three multiple membership multilevel negative binomial models to reduce unobserved zonal-level heterogeneity. Each multiple membership multilevel model used a different weight strategy. When the fitting performance of the three multiple membership multilevel models was compared with two additional models, a traditional single level model and a conventional multilevel model, all three multiple membership multilevel models had a better fitting performance. Five individual-level and seven group-level variables were statistically significant (90% confidence level) in all the models with five of the individual-level and four of the group-level variables statistically significant at the 99% confidence level. The multiple membership multilevel models also helped to prevent the underestimation of group-level variance and type I statistical errors that tend to occur with single level models and conventional multilevel models. In particular, the three multiple membership multilevel models produced more accurate results for intersections with a large AADT. As intersections with a large AADT are known to have more crashes, multiple membership multilevel models are likely to be more useful than single level models and conventional multilevel models when selecting intersections for safety improvement. The study recommends the adoption of a multiple membership multilevel model to improve fitting performance and reduce the boundary problem for intersections affected by more than one zone.