Generalized P-Values Test In Mixed Effects Models

Linear mixed effects model is a kind of statistical model that was widely used in biology, medicine and economics.When a nuisance parameter is present for testing some parameters in the models, the p-value based on the well-behaved test statistic may depend on the nuisance parameter and hence cannot be used.The concept of generalized p-value was introduced by Tusi and Weerahandi (1989), and since then the novel concept has been applied to solve a number of problems when conventional methods are difficult to apply or fail to provide exact solutions.This article is based on the generalized p-value theory for testing some parameters of linear mixed model.The problems of testing hypotheses on the fixed effects and variance components in linear mixed effects models have been addressed by various researchers, althrough exsiting methodology is still restricted to a narrow range of models.For example, some literatures constructed confidence intervals for the variance component and the nonuniqueness of the generalized test variable for testing occurs which depends on positive constants. It still remains unsolved how to choose these constants.In this paper, we first develop a generalized p-values test in regression models with nested error under heteroscedasticity.On the other hand, we develop new general p-value tests for complex hypotheses in the general linear mixed effects models with two variance components. The p-values are motived by a useful martix inequality, and the method is extended to general p-value tests in the linear mixed effects models with multiple variance components. Moreover,our proposed approach do not need to select appropriate or optimal weights. It appears that the tests based on generalized p-value can control the Type I errors satisfactorily and exhibit good power properties not only for the balanced case but also for the unbalanced case. Furthermore, the new methods are simple and easy to apply.