Overdispersion Test Based On Generalized Linear Model

Testing for overdispersion is very important and necessary in the analysis of count data.For the different models used in the analysis,various methods are available to test for overdispersion and all have their advantages and disadvantages.In this thesis,by using Monte Carlo simulation and empirical analysis methods,the superiority of the LRT test,Score test and Bootstrap test in the negative binomial regression model and Zero-inflated negative binomial regression model are studied.There are five chapters in this thesis.The chapter one is general introduction,where background information and significance of the research are introduced along with information on the content and structure of the study.In the chapter two,some basic models in the analysis of count data,such as Poisson regression model,negative binomial regression model and zero-inflated negative binomial regression are introduced.We also introduced some basic information about overdispersion,including the definition of overdispersion and three common tests for overdispersion: the LRT test,Score test and Bootstrap test.In the chapter three,by using Monte Carlo simulation and empirical analysis,the superiority of LRT test,Score test and Bootstrap test are compared,based on the negative binomial regression with covariates and without covariates.The results show: All three methods can detect overdispersion within data with certain effectiveness.For small samples,the Bootstrap test is the best among three in terms of power.Covariates have a positive effect on the power of the test,meaning for each test,it is more powerful under the negative binomial regression model with covariates than without covariates.In the chapter four,by using Monte Carlo simulation and empirical analysis,the power and type I error of LRT test,Score test and Bootstrap test are compared,based on the zero-inflated negative binomial regression model on the overdispersion and zero-inflated count data.The results show: Under the experimental condition,the Bootstrap test performs best in terms of both the power and the type I error;For all three tests,under any given dispersion,the greater the degree of zero-inflation,the lower the power of test and the larger the mean of zero-inflated negative binomial regression model,the more powerful the test.At the end,the research results are summarized along with some thoughts and suggestions for future research.