Zero-Inflated Poisson Regression for Longitudinal Data

Abstract

Medical and public health research often involve the analysis of repeated or longitudinal count data that exhibit excess zeros such as the number of yearly doctor visits by a group of individuals over a number of years. Zero-inflated Poisson (ZIP) regression models can be used to account for excess zeros in count data. We propose an extension of the ZIP model that is appropriate for longitudinal data. Our extension includes a non stationary, observation-driven time series model based correlation structure. We discuss estimation of the model parameters and the inefficiency of the estimators when the correlation structure is mis-specified. The model's application to the analysis of health care utilization data is also discussed.

Keywords:

• AR(1)
• MA(1)
• and exchangeable correlation structures
• Generalized quasi-likelihood
• Non stationary
• Zero-inflated Poisson

Mathematics Subject Classification:

• 62F10
• 62M10

Acknowledgments

This research is partially supported by Natural Sciences and Engineering Research Council of Canada and University Research Fund and Start-up fund, University of New Brunswick. The authors thank the Associate Editor and referee for their comments and suggestions that improved the quality of the manuscript. The authors also thank Professor B. C. Sutradhar for providing the health care data.