Variance Component Of The Mixed Model Of Generalized Single Indicator Test

In the regression analysis,it is common to assume the independence and homoscedasticity of the observation responses.In generalized parametric and nonparametric models,there is no need to test the homoscedasticity of the model. However,the test on the variance components attracts many researchers' interests. In this paper,the variance component for mixed generalized single index models is tested on the basis of Penalized Spline estimation.Based on this ideology,in chapter 2,with the introduction of P-spline estimation, knots selection theory and penalized likelihood ratio function,Score statistic for testing dispersion parameter is derived,followed by the verification of effectiveness by simulations.In many exponential models,Random effect is another main cause for over or under-dispersion of variance.So in chapter 3,the variance component test in discrete generalized single index model with random effects for longitudinal data is studied.Simulation for the score testing statistics is also illustrated.