Parameter estimation and inference in linear mixed models

Although the most widely-used statistical model is the linear regression model, it is sometimes possible to encounter with the data structures that accord with the models that include both fixed and random effects. In this case, linear mixed models are arised. Linear mixed models are an important tool for the analysis of a broad variety of data including clustered data and longitudinal (repeated measures) data. In this study firstly, linear mixed models, assumptions of linear mixed models, parameter estimations in linear mixed models, model building process for repeated measures data, variance-covariance models in literature and selection criteria of appropriate model among these variance-covariance models have been examined. Later, the mixed, stochastic restricted ridge, Liu, principal components regression and r-k class estimators and predictors have been proposed alternative to the ridge estimator and predictor in linear mixed model literature when there is multicollinearity and performances of estimators and predictors have been compared by using the matrix mean square error criterion. The study is supported with applications done using R and Matlab R2014a programs.