Statistics of score tests for detecting excess Poisson variance

Abstract

When the empirical variance in the data is higher than that expected by the model, count data examined under a Poisson assumption or data in the form of proportions under a binomial assumption sometimes demonstrate overdispersion. Underestimating standard errors of covariate e_ects is one of the implications of neglecting overdispersion. This paper involves a selective overview of score test statistics that are existing literature and used to detect the extra-Poisson variation. The methodologies of these tests have been covered to aid the statistics practitioners in understanding how to deal with count data and identify whether there is extra-Poisson variation. The baseline formula of all score test statistics had been derived from the negative binomial model. Subsequently, the proposed adjusted test statistics have been presented to approximate the distribution of these tests to standard normal distribution. However, the test result is unreliable unless the correct conditional mean and variance are obtained