Count Regression Models with an Application to Zoological Data Containing Structural Zeros

Ilknur Ozmen,Felix Famoye

doi:10.6339/jds.2007.05(4).385

Abstract

Recently, count regression models have been used to model over dispersed and zero-inflated count response variable that is affected by one or more covariates. Generalized Poisson (GP) and negative binomial (NB) regression models have been suggested to deal with over-dispersion. Zero inflated count regression models such as the zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) and zero-inflated generalized Pois son (ZIGP) regression models have been used to handle count data with many zeros. The aim of this study is to model the number of C. caretta hatchlings dying from exposure to the sun. We present an evaluation frame work to the suitability of applying the Poisson, NB, GP, ZIP and ZIGP to zoological data set where the count data may exhibit evidence of many zeros and over-dispersion. Estimation of the model parameters using the method of maximum likelihood (ML) is provided. Based on the score test and the goodness of fit measure for zoological data, the GP regression model performs better than other count regression models.

Highlights

Poisson regression is a standard model for analysis of count data
To understand how the different count regression models fit the zoological data, we examine the fit of various regression models to the number of C. caretta hatchlings dying from exposure to the sun
Is the zero-inflated Poisson (ZIP) regression model statistically preferred over the Poisson regression model? We apply the score test to check whether the ZIP regression model is a significant improvement over the Poisson regression model

Summary

Introduction

Poisson regression is a standard model for analysis of count data. While the Poisson regression model may be the foremost candidate, it rarely explains the data due to several important constraints. One important constraint in the Poisson regression model is that the mean of the distribution must be equal to the variance If this assumption is not valid, the standard errors, usually estimated by the ML method, will be biased and the test statistics derived from the models will be incorrect. In overcoming the problem of over-dispersion, several researchers (Lawless, 1987; Famoye, 1993) employed the NB and GP regression models instead of the Poisson regression model. In these regression models, the estimates of the regression parameters are obtained by incorporating a dispersion parameter

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