Comparison of two-level hlm estimators via mc simulations: reml vs minque

The purpose of the study was to compare the performance of two estimation procedures, REML and MINQUE, for a two-level hierarchical linear model. It was expected that the variance-covariance components estimates provided by MINQUE procedure will have less bias then those obtained by REML when the normality can not be guaranteed. The investigated MINQUE method attained three types of a piori values -- MINQUE(0), MINQUE(1) and MINQUE(theta). A special focus was on hierarchical structure of TIMSS data. The design of TIMSS data was taken into account while creating the simulation design of this study. Procedures were tested under various sample sizes and random effects covariances. Applying Monte Carlo simulations it was shown that except for a small range REML and MINQUE procedures provided almost identical results regardless of the distribution of model residuals and random effects. PWMINQUE procedure was developed in the process. This procedure takes into account sample weights and was based on PWIGLS procedure. PWMINQUE was tested through MC simulations and provided less bias than unweighted procedures in the case of informative sampling. Taking into account the obtained results two-level HLM model for eight grade TIMSS 2011 data of Lithuania was constructed. This model was estimated by REML and MINQUE procedures