Algorithm Overview and Design for Mixed Effects Models

Linear Mixed Model (LMM) is an extended regression method that is used for longitudinal data which has repeated measures within the individual. It is natural to expect high correlation between these repeats over a period of time for the same individual. Since classical approaches may fail to cover these correlations, LMM handles this significant concern by introducing random effect terms in the model. Besides its flexible structure in terms of modeling, LMM has several application areas such as clinical trials, genetics, neurosciences, economy, etc. However, the statistical inference procedure of the model may not always generate closed form solutions of the parameter estimations. Therefore, a large number of estimation techniques and computational strategies are adapted in LMM such as Expectation Maximization algorithm. Also, even the main inferential tool is likelihood method for the LMM, the implementation of the method may change depending on the data structure (balanced/unbalanced), covariance structure or the distributional assumptions. It is possible to see these methods in many different sources, but it is not always easy to see which one will be used in what kind of situations and in what direction the results will change. In this study, we systematically categorize these algorithms and compare them in terms of efficiency and time for longitudinal data sets