Model Selection for Linear Mixed Models Using Predictive Criteria

Predictive criteria, including the adjusted squared multiple correlation coefficient, the adjusted concordance correlation coefficient, and the predictive error sum of squares, are available for model selection in the linear mixed model. These criteria all involve some sort of comparison of observed values and predicted values, adjusted for the complexity of the model. The predicted values can be conditional on the random effects or marginal, i.e., based on averages over the random effects. These criteria have not been investigated for model selection success.

We used simulations to investigate selection success rates for several versions of these predictive criteria as well as several versions of Akaike's information criterion and the Bayesian information criterion, and the pseudo F-test. The simulations involved the simple scenario of selection of a fixed parameter when the covariance structure is known.

Several variance–covariance structures were used. For compound symmetry structures, higher success rates for the predictive criteria were obtained when marginal rather than conditional predicted values were used. Information criteria had higher success rates when a certain term (normally left out in SAS MIXED computations) was included in the criteria. Various penalty functions were used in the information criteria, but these had little effect on success rates. The pseudo F-test performed as expected. For the autoregressive with random effects structure, the results were the same except that success rates were higher for the conditional version of the predictive error sum of squares.

Characteristics of the data, such as the covariance structure, parameter values, and sample size, greatly impacted performance of various model selection criteria. No one criterion was consistently better than the others.