A new approach to truncated regression for count data

Abstract

Standard Poisson and negative binomial truncated regression models for count data include the regressors in the mean of the non-truncated distribution. In this paper, a new approach is proposed so that the explanatory variables determine directly the truncated mean. The main advantage is that the regression coefficients in the new models have a straightforward interpretation as the effect of a change in a covariate on the mean of the response variable. A simulation study has been carried out in order to analyze the performance of the proposed truncated regression models versus the standard ones showing that coefficient estimates are now more accurate in the sense that the standard errors are always lower. Also, the simulation study indicates that the estimates obtained with the standard models are biased. An application to real data illustrates the utility of the introduced truncated models in a hurdle model. Although in the example there are slight differences in the results between the two approaches, the proposed one provides a clear interpretation of the coefficient estimates.