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

摘要

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.