Limitations of ordinary least squares models in analyzing repeated measures data

To a) introduce and present the advantages of linear mixed models using generalized least squares (GLS) when analyzing repeated measures data; and b) show how model misspecification and an inappropriate analysis using repeated measures ANOVA with ordinary least squares (OLS) methodology can negatively impact the probability of occurrence of Type I error. The effects of three strength-training groups were simulated. Strength gains had two slope conditions: null (no gain), and moderate (moderate gain). Ten subjects were hypothetically measured at five time points, and the correlation between measurements within a subject was modeled as compound symmetric (CS), autoregressive lag 1 (AR(1)), and random coefficients (RC). A thousand data sets were generated for each correlation structure. Then, each was analyzed four times--once using OLS, and three times using GLS, assuming the following variance/covariance structures: CS, AR(1), and RC. OLS produced substantially inflated probabilities of Type I errors when the variance/covariance structure of the data set was not CS. The RC model was less affected by the actual variance/covariance structure of the data set, and gave good estimates across all conditions. Using OLS to analyze repeated measures data is inappropriate when the covariance structure is not known to be CS. Random coefficients growth curve models may be useful when the variance/covariance structure of the data set is unknown.