Tests For Fixed Effect In Mixed Linear Models

Linear mixed model is a kind of statistical modelon on its strong characteristic of applica-bility, the issue of hypothesis testing in this model has drawn scholars'attention. For testing the regression coefficient is need in the variable selections and judgements of the validity of the linearity of the models. When the variance components are known,there are uniformly pow-erful.But in actual fact,they are often unknown and are substituted with estmates. Different test statistics come from different estimating methods,and their test sizes and power functions are unknown because of their unknnown distributions. The generalized p value and generalized confidence interval due to Tsui and Weerahandi are nimble and effective approaches to solve the testing problems with nuisance parameters.In this paper, we consider the testing problems of fixed effect in mixed models by using the concepts of generalized p value.Also tests is proposed in the balanced models by using the combining testing.In chapter two,we study the problem of testing the regression coefficients the non-homogeneous linear hypothesis in the balanced linear mixed model with nested error structure.First,get three new singular linear models by linear transformations for model,and,then get independent esti-mates of fixed effects and variance components from the three new models. then we obtaine the exact tests and confidence intervals based generalized p value theoreticalmethod, and the result is generalized to the general balance of linear mixed model. Meanwhile, for the problem ,we also use a combination of test methods by Cohen-Sackrowitz(1989), has been construct a precise combination of test. Finally we discuss theses tests under scal transformation simulating the effectiveness of the simulation results show that the two tests have a better effect.In chapter three, we study the problem of testing the regression coefficients the non-homogeneous linear hypothesis in the unbalanced two-way mixed models with interaction effect. First, in or-der to discuss the interval estimation of the among group variance the statistic which is called unweighted sum of squares (USS) was constructed using the method of Khuri(1998). Then by the generalized approach,we derive the generalized pivot of fixed effects, by which the gener-alized p-value and generalized confidence regions are defined directly. Finally a Monte Carlo simulation was conducted to illustrate the test dominates the type Ierror very well. In addition, an practical example are provided to illustrate computations.