Statistical Diagnostics. Exponential Family Semiparametric Nonlinear Random Effects Model

Semi-parametric model and random effects model, useful in many problems especially for biometric and econometric applications, become an important research field in the regression. This paper present the exponential semi-parametric nonlinear and random effects model, especially for the method and application of the diagnostic. The Gauss-Newton iteration algorithm for the models' estimations is given at first. Then, we get the concise diagnostic expressions based on case deletion or subject deletion model, establish an equivalence between the case deletion model and mean shift outlier model form which we derive tests for outliers. We also discuss the local influence and get concise influence matrix. At last we derive the test for varying dispersion of the exponential semi-parametric nonlinear model. Numerical examples are given to illustrate our results.