Model selection in linear mixed-effects models

Most recently published work has utilized Diggle's heuristic three-step selection procedure for model selection when doing normal linear mixed-effects model analysis. In general, there appears to have been little investigation of the relative performances of the alternative methods that can be adapted for model selection with normal linear mixed-effects models.; Consequently, this dissertation is focused on the application, refinement where needed, and evaluation of alternative methods for model selection of linear mixed-effects models. The implementation of the Kullback-Liebler-based information criterion TIC (Tageuchi Information Criterion) was carried out in both cases of linear models and linear mixed-effects models. A simulation algorithm for linear mixed-effects models was designed to generate the needed simulated data sets. Although it is based on less restricted theoretical assumptions than AIC (Akaike Information Criterion), TIC's performance through simulation studies suggests that TIC, in practice, does not perform better than AIC even though TIC has greater computational requirements. Both TIC, and AIC tend to overestimate the dimension of the mean and variance-covariance structure of the true linear mixed-effects model. Simulation results for CAIC (Consistent Akaike Information Criterion) for linear models and linear mixed-effects models using the full maximized likelihood show that CAIC performs better than either TIC or AIC.; However, there has been some ambiguity about what should be used for the "effective sample size" when computing CAIC with repeated-measures data. Computation of the effective sample size based on the asymptotic order of information of the information matrix was carried out for linear mixed-effects models, and the computed effective sample size was used in CAIC. A four-step model selection algorithm for linear mixed-effects models was suggested, and was illustrated in two case studies.