Power of Tests for Overdispersion Parameter in Negative Binomial Regression Mode

Abstract

In this paper we focus on a negative binomial (NB) regression model to take account of overdispersion in Poisson counts. Moreover, we present the power of score test for testing the overdispersion parameter in the negative binomial regression model. The power of the proposed score test was compared with the LRT and Wald test via Monte Carlo simulation technique using SAS 9.2 software. The application of the test was shown using two real datasets such as using numerical illustration and real datasets. Keywords- Count data, Negative binomial regression, Overdispersion, Score test I. INTRODUCTION Poisson regression is one of the most popular techniques for the analysis of count data. Whereas the Poisson regression model may be the foremost candidate, it rarely explains the data due to several important constraints. One important constraint is the mean of the distribution must be equal to the variance. In this case the standard errors, usually estimated by the Maximum Likelihood method, will be biased and the test statistics derived from the models will be incorrect. Therefore, this problem leads an overdispersion. Failure to take overdispersion into account leads to serious underestimation of standard errors and misleading inference for the regression parameters. Consequently, a number of models and associated estimation methods have been proposed for handling overdispersed data. Such models include those based on the negative binomial distributions as well as regression models based on mixtures of Poisson (Lawless