Effects of Multicollinearity in All Possible Mixed Model Selection

The effects of multicollinearity in all possible model selection of fixed effects including quadratic and cross products in the presence of random and repeated measures effects are presented here. The user-friendly SAS macro application ALLMIXED2 complements the model selection option currently available in the SAS macro applications ‘REGDIAG’ and ‘LOGISTIC’ for multiple linear and logistic regressions respectively. Options are also available in this macro to select the best covariance structure associated with the user-specified fully saturated repeated measures model; to graphically explore and to detect statistical significance of user specified linear, quadratic, interaction terms for fixed effects; and to diagnose multicollinearity, via the VIF statistic for each continuous predictors involved in each model selection step. The effects multicollinarity and sample size in pre-screening the variables in GLMSELECT using the LASSO selection method and in all possible subset selection within user-specified subset range are investigated using simulated repeated measures data with time independent auto-correlated error structure. A combination of two sample sizes (25 and 100 subjects) and two levels of mulicollinarity ( r < 0.2 and r > 0.8) among selected covariates were used in simulating 4 repeated measures data sets. Two model selection criteria, AICC (corrected Akaike Information Criterion) and MDL (minimal description length) were used in all possible model selection and summaries of the best model selection are compared graphically. The outcome of the model selection based on information criteria (AICC or MDL) was not influenced by the degree of multicollinarity. However, the sample size had a major impact on the accuracy of best candidate model selection. Instructions for downloading and running this user-friendly macro application, ALLMIXED2 are included.