INTRODUCTION

In this chapter we provide a detailed discussion of empirical models for three examples based on four cross-sectional data sets. The first example analyzes the demand for medical care by the elderly in United States and shares many features of health utilization studies based on cross-section data. The second example is an analysis of recreational trips. The third is an analysis of completed fertility – the total number of children born to a woman with a complete history of births.

Figure 6.1 presents histograms for the four count variables studied; the first two histograms exclude the highest percentile for readability. Physician visits appear roughly negative binomial, with a mild excess of zeros. Recreational trips have a very large excess of zeroes. Completed fertility in both cases is bimodal, with modes at 0 and 2. Different count data models will most likely be needed for these different datasets.

The applications presented in this chapter emphasize fully parametric models for counts, an issue discussed in section 6.2. Sections 6.3 to 6.5 deal, in turn, with each of the three empirical applications. The health care example in section 6.3 is the most extensive example and provides a lengthy treatment of model fitting, selecting, and interpreting, with focus on a finite mixture model. The recreational trips example in section 6.4 pays particular attention to special treatment of zero counts versus positive counts. The completed fertility illustration in section 6.5 is a nonregression example that emphasizes fitting a distribution that is bimodal. Section 6.6 pursues amethodological question concerning the distribution of the LR test under nonstandard conditions, previously raised in Chapter 4.8.5.