UCLA

Linear mixed effects models have been widely used in different disciplines and have become a large research field of Statistics. With the development of science and technology, a large amount of variables are always available to choose for a model and it is necessary to control the numbers of variables to avoid the overfitting problem and use the most efficient way to explain data. Most methods published pay more attention to the selection and estimation of fixed effects but it is meaningful to get a deep insight into variable selection for random effects. Some adjustments have been made in this thesis to obtain the specific methods for variable selection on random effects model based on reviews of some classic or latest methods for variable selection on mixed effects model. These methods and algorithms have been applied on some simulation data and compared through changes on number of subjects and observations. Additionally, these methods have been applied into a real world dataset to study how some effects will influence the democracy index among different countries.