HETEROGENEITY, EXCESS ZEROS, AND THE STRUCTURE OF COUNT DATA MODELS

TLDR

The paper shows that unobserved heterogeneity, assumed to cause overdispersion in count data models, predicts specific probability structures. The authors propose test statistics to detect heterogeneity‑related departures from the null model and apply them to a health‑care utilization example, indicating that a null Poisson model should be rejected in favor of a mixed alternative. Excess zeros are a strict implication of unobserved heterogeneity, underscoring the importance of using count model estimates for predicting certain parameters. © 1997 John Wiley & Sons, Ltd.

Abstract

This paper demonstrates that the unobserved heterogeneity commonly assumed to be the source of overdispersion in count data models has predictable implications for the probability structure of such mixture models. In particular, the common observation of excess zeros is a strict implication of unobserved heterogeneity. This result has important implications for using count model estimates for predicting certain interesting parameters. Test statistics to detect such heterogeneity-related departures from the null model are proposed and applied in a health-care utilization example, suggesting that a null Poisson model should be rejected in favour of a mixed alternative. © 1997 John Wiley & Sons, Ltd.