Multi-Threhold Negative Binomial Regression Model

We propose a multi-threshold negative binomial regression model and use a two-stage procedure with an iterative process to estimate the location of thresholds and model parameters. In the first stage we use a group selection method to identify the number of thresholds, then in the second stage, thresholds locations and estimates of model parameters are obtained. We examine the performance of the proposed methods by simulation studies and provide an illustration using crash data.