The Testing of Random Effect in Mixed Generalized Single Index Models

In the regression analysis, it is common to assume the independence and homogeneous of the observation responses. In generalized parametric and nonparametric models, there does not exist the homoscedasticity of the model. However, in many exponential models, random effect is another main cause for over or under-dispersion of variance. So in this paper, the testing of random effect in discrete generalized single index model with random effects for longitudinal data is studied. Simulation for the Score testing statistics is also illustrated.