Many road safety researchers have used crash prediction models, such as Poisson and negative binomial regression models, to investigate the associations between crash occurrence and explanatory factors. Typically, they have attempted to separately model the crash frequencies of different severity levels. However, this method may suffer from serious correlations between the model estimates among different levels of crash severity. Despite efforts to improve the statistical fit of crash prediction models by modifying the data structure and model estimation method, little work has addressed the appropriate interpretation of the effects of explanatory factors on crash occurrence among different levels of crash severity. In this paper, a joint probability model is developed to integrate the predictions of both crash occurrence and crash severity into a single framework. For instance, the Markov chain Monte Carlo (MCMC) approach full Bayesian method is applied to estimate the effects of explanatory factors. As an illustration of the appropriateness of the proposed joint probability model, a case study is conducted on crash risk at signalized intersections in Hong Kong. The results of the case study indicate that the proposed model demonstrates a good statistical fit and provides an appropriate analysis of the influences of explanatory factors.