The objective of this paper is to evaluate the impact of various risk factors on traffic crashes presenting different collision types at freeway diverge areas. Three-year period crash data from 367 freeway diverge areas were obtained. Three types of collisions, including rear-end, sideswipe, and angle collisions, were considered. A random parameters multivariate Poisson-lognormal (RP-MVPLN) model was developed to accommodate both correlations between crashes across collision type and the unobserved heterogeneity across observations. For the performance comparison, an MVPLN was developed and compared with the RP-MVPLN model under the Bayesian framework. The result showed that the RP-MVPLN model outperformed the MVPLN model, which highlighted that accounting for the unobserved heterogeneous effects of risk factors could improve the model fit. The model estimation result showed that the risk factors, as well as their impacts on different collision types, were different. The mainline annual average daily traffic (AADT), the lane-balanced design, and the number of lanes on the mainline were found to be significantly associated with all types of collisions, whereas the deceleration lane length and road surface type only affected rear-end crashes. The exit ramp length and ramp AADT had significant impact on rear-end crashes and sideswipe crashes, but they did not affect angle crashes. The speed limit was negatively related with rear-end crashes and angle crashes, while it had no impact on sideswipe crashes. Three risk factors, which are the mainline AADT, ramp AADT, and speed limit, were found to have significant heterogeneous effects on crashes across observations. INDEX TERMS Collision type, freeway diverge area, random parameters, multivariate model, full Bayesian estimation.