The linear mixed model is widely implemented in the analysis of longitudinal data. Inference techniques and information criteria are available and well-studied for goodness-of-fit within the linear mixed model setting. Predictive approaches such as R-squared, PRESS, and CCC are available for the linear mixed model but require more research (Edward, 2005). This project used simulation to investigate the performance of R-squared, PRESS, CCC, Pseudo F-test and information criterion for goodness-of-fit within the linear mixed model framework. Marginal and conditional approaches for these predictive statistics were studied under different variance-covariance structures. For compound symmetry structure, the success rates for all 17 statistics (marginal and conditional R-squared, PRESS, CCC, F test, AIC and BIC) were high. The study suggested using marginal rather than conditional residuals for PRESS, CCC and R-squared. It suggested using REML likelihood function which has the determinant term for AIC and BIC. For CCC, R-squared, and the information criterion, there was no difference for the various parameter number adjustments. For autoregressive order 1 plus random effect, the study suggested using conditional residuals for PRESS, marginal residuals for CCC and R-squared, and using REML function with the determinant term for AIC and BIC. Also there was no difference for the different parameter number adjustments. The F-test performed well for all covariance structures. The study also indicated that characteristics of the data, such as the covariance structure, parameter values, and sample size, can greatly impact performance of various statistics. No one criterion is consistently better than the others in terms of selection performance in the simulation study.



College and Department

Physical and Mathematical Sciences; Statistics



Date Submitted


Document Type

Selected Project




mixed model, model selection, predictive approaches, AIC, BIC, F-test