Testing For Varying Dispersion And Analysis Of Sensitivity In Poisson-Gamma Models Based On Longitudinal Data

In ordinary regression analysis with random effects, the homoscedasticity of random effects is a basic assumption. Under this assumption, it is feasible to make routine statistical inference. If the variances of random effects are heteroscedastic and unknown, then the regression analysis will meet many troubles. In the analysis of longitudinal data, when the clusters size are random, it is still a conventional hypothesis that random effects should have homoscedasticity, Otherwise statistical inference would be more difficult. However, the rationality of this assumption of homoscedasticity of random effects is doubtable. Therefore the verification for heteroscedasticity of random effects is absolutely necessarily and important for dealing with the regression problems in theory and practice.Concretely, the main result and originality of this paper are shown as follows:Chapter 2 are devoted to the investigation of Poisson-Gamma regression model with random clusters. By employing the method of variances parameterization, we consider the test for the heteroscedasticity of random effects under the condition of random clusters.In chapter 3 we study the Poisson-Gamma model with longitudinal data by using the random coefficient method. Because the coefficient distribution is unknown, it is difficult to get the response variable distribution. We apply the Laplace method to get the asymptotic distribution, based on which the score statistics are obtained. At the end of this chapter, numerical example and corresponding Monte Carlo simulations are gived to show the validity of all test statistics we get here.Chapter 4 is assigned to the analysis of the sensitivity of test for overdispersion in Poisson nonlinear regression model with longitudinal data, and the inference function is obtained. Also concrete numberical example is used to illustrate the effectiveness of the proposed function.In summary, on the basis of the research about ordinary Poisson-Gammaon regression models, we study the tests for the heteroscedasticity of random effects and analyze the sensitivity of test for overdispersion. We illustrate the practicality of the test statistics with an application to Monte Carlo simulation.