Validation Of The Estimation Of Variance Components And Generalized P Values In The Linear Mixed Model

The linear mixed model is a widely used statistical model. In the present study the author first investigated the Analysis of Variance (ANOVA) estimate of the random effects linear mixed model with three variance components, and discussed the condition under which this estimate is consistently better than ANOVA with the mean square loss. Given that the probability of this ANOVA estimate to yield a negative value is greater than none, the author restricted the estimation using a specific non-negative value to obtain the non-negative estimation of variance components, and provided the condition that is necessary and sufficient for this restricted estimation, with the mean square loss, to be better than the original estimation. Secondly, incorporating the concept and the approach of the generalized p value and the generalized confidence interval, the author established an accurate validation for the hypothesis testing of regression coefficients in the Panel data model with interaction effects, determined several generalized confidence intervals for the coefficient of regression, and discussed the consistency of the established confidence intervals with variable scaling parameters.