Mixed Effects Model Of Hypothesis Test

Mixed effects model is a kind of applied statistical model, the model have been applied in the biological, medical, economic, financial, environmental science and engineering technology, and thus attracted many researcher’s extensive attention and application. In this paper,we focuses on the hypothesis test of fixed effects and random effects in the mixed effects model.In chapter two, we study the hypothesis for the variance component is equal to zero or not in one-way random effects model. We mainly used the parametric bootstrap method to solve this testing problem. At the same time, this method solved the problem of generalized p value which cannot guarantee the testing level. First, according to the estimation of the model generate the bootstrap samples. And then construct a parametric bootstrap testing pivot. At last, calculate the p-value.In third chapter we consider the Two-Way ANOVA model with unequal cell frequencies without the assumption of equal error variances. For the problem of testing no interaction effects and equal main effects, we propose a parametric bootstrap approach and compare it with the existing the generalized p value test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the generalized p value test. The PB test performs very satisfactorily even for small samples while the generalized p value test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up.