Mixed Effects Model Of Statistical Inference And Application

In this paper, we mainly study the test of fixed effects and random effects in the mixed effects model, the main methods are based on the theory of generalized p-values and ideas on parametric bootstrap, and the datum simulated of the proposed tests are given. The generalized p-value is also applied for testing the common mean of several inverse Gaussian populations.The mixed effects model provides a powerful tool in analyzing complex datum, for example, clustered data, longitudinal data, repeated measurement data and block data. The purpose of testing the significance of variance components in mixed effects model is to know whether there are the corresponding random effects, and the purpose of testing the fixed effects is to choose variables.In this paper, the hypothesis for variance component is the variance is smaller than or equal to a specified nonnegative value, not to test whether the variance is zero. A parametric bootstrap method to test the significance of random effects in one-way random effects model is given, this approach solves the problem of the generalized p-value method. We define a measure to interaction in two-way mixed effects model to test the negligible interaction, and derive the classical F-test and generalized p-value test, the simulated results prove that these two methods have good performance at controlling Type I error rates. The article develops generalized p-value method to test the main effects, and the algorithm of power function is given.For the one-way fixed effects model, a new parametric bootstrap statistic is developed to test the equality of fixed effects, and compared with the generalized p-value test, the results prove that the PB method is better than the generalized p-value test when the sample sizes k goes up. A generalized p-value method is also applied for testing the common mean of several inverse Gaussian populations, the test model is essentially equal to one-way fixed effects model, and power function is satisfactory which simulated by Monte-Carlo method. Wald-type test and generalized p-value test based on spectral decomposition estimation are proposed for testing the fixed effects.