Ridge and restricted estimation methods in linear mixed models: A Monte Carlo simulation study

Linear mixed model can be thought of as extended linear regression model. Although in linear regression model only fixed effects take place, in linear mixed models both fixed effects and random efffects occur. In this study, linear mixed model types and parameter estimates are featured. The maximum likelihood and restricted maximum likelihood methods to estimate variance components are discussed. In linear mixed models, methods that identify variance-covariance structure of dependent variable are examined in detail and information criterions are utilized to select the appropriate model. In linear regression model, multicolinearity problem and its impact on statistical results are well known. Similiar results can also be seen on fixed effect parameters that take place in linear mixed models. In this study, restricted and ridge estimation methods which are the estimation methods that are used in the case of multicollinearity are given as alternatives to linear mixed models. Estimates obtained by restricting fixed effects and random effects parameters are compared with BLUE and BLUP. Additionly, a theorem is developed that gives necessary and sufficient conditions for the ridge mixed model estimator to be superior to the mixed estimator. In practical part of the study, a set of data in health field is examined and the theorical findings that has been obtained are interpreted and analysed with the support of Matlab 2012, IBM SPSS Statistics 22 and Excel programs. In addition, the study was supported by Monte Carlo simulation study that was implemented on Matlab 2012 program.