On The Efficiency of Maximum Likelihood and Restricted Maximum Likelihood Estimators For Linear Mixed Effects Models

In this work, the performances of maximum likelihood (ML) and restricted maximum likelihood (REML) estimation of linear mixed effects models were examined. The behaviors andProperties of the ML and REML methods of estimating the variance-covariance components in linear mixed-effects models were studied via Monte-Carlo experiment. Results revealedthat both estimation techniques yielded the same estimates of the fixed effect parameters. However, ML estimates of variance-covariance components, especially for the randomeffects terms were more biased downwards than the REML counterparts. It was also discovered that the bias of the ML estimates for the variance-covariance components increasesas the number of fixed eects parameters in the model increases.