Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model

Enas Gawdat Yehia

doi:10.11648/j.ajtas.20211003.13

Abstract

Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.

Highlights

The counting data can be defined as the number of occurrences of an event within a fixed period of time, where which this data can take only non-negative discrete numbers
Overdispersion is often encountered in count regression which leads to poor fit when inference about regression parameters
The empirical power for statistics of these tests was assessed under different levels of overdispersion by Monte-Carlo simulation

Summary

Introduction

The counting data can be defined as the number of occurrences of an event within a fixed period of time, where which this data can take only non-negative discrete numbers. Poisson regression is the most common modeling technique for count data in a wide variety of fields such as biostatistics, agriculture, econometric, epidemiology, psychology, and many others. The standard Poisson regression models have the equidispersion limitation which the mean and variance of counts are equal. Many count data do not satisfy the equidispersed property, they are either overdispersed (variance is greater than mean) or underdispersed (variance is less than mean) Cameron and Trivedi [4]. The negative binomial regression is an appropriate approach to model overdispersed count data as an alternative to Poisson regression model.

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