INTRODUCTION

It is desirable to analyze count data using a cycle of model specification, estimation, testing, and evaluation. This cycle can go from specific to general models – for example, it can begin with Poisson and then test for the negative binomial – or one can use a general-to-specific approach, beginning with the negative binomial and then testing the restrictions imposed by Poisson. In terms of inclusion of regressors in a given count model, either approach might be taken; for the choice of the count data model itself, other than simple choices such as Poisson or negative binomial, the former approach is most often useful. For example, if the negative binomial model is inadequate, there is a very wide range of models that might be considered, rendering a general-to-specific approach difficult to implement.

The preceding two chapters have presented the specification and estimation components of this cycle for cross-section count data. In this chapter we focus on the testing and evaluation aspects of this cycle. This includes residual analysis, goodness-of-fit measures, and model specification tests, in addition to classical statistical inference.

Residual analysis, based on a range of definitions of the residual for heteroskedastic data such as counts, is presented in section 5.2. A range of measures of goodness of fit, including pseudo R-squareds and a chi-square goodness-of-fit statistic, is presented in section 5.3. Discrimination among nonnested models is the subject of section 5.4.