The increased use of repeated measures for longitudinal studies has resulted in the necessity for more research in the modeling of this type of data. In this dissertation, we extend three candidate model selection methods from the univariate linear model to the linear mixed model, and investigate their behavior. Mallows' Cp statistic was developed for the univariate linear model in 1964. Here we propose a Cp statistic for the linear mixed model and show that it can be a promising method for fixed effects selection. Of all the methods investigated in this dissertation, the Cp statistic gave the most favorable results in terms of fixed effects selection and is the least computationally demanding of all the candidate methods. The KIC statistic, a symmetric divergence information criteria, explored here appears to be promising as a model selection method for both fixed effects and covariance structure. In the selection of the correct covariance structure, the KIC tended to hold middle ground between the AIC and the BIC. In terms of fixed effects, the KIC appears to perform significantly better than either the AIC or BIC in the selection of fixed effects when there is no interaction effect present. The predicted sum of squares (PRESS) statistic has been developed for the linear mixed model and is available in the SAS statistical software, but its abilities as a model selection method lacked sufficient evaluation. From our study, it appears that the PRESS statistic does not add much as a fixed effect selection method compared to the Cp or the KIC while being more computationally intensive. All three criteria are investigated using simulation studies and a large example dataset evaluating health outcomes in the elderly to determine their reliability. As a by-product of this research, the reliability of standard selection criteria in the linear mixed model, namely the AIC and BIC, are also evaluated. Numerous areas of future research within the context of model selection methods in the linear mixed model, are identified
