Limitations of ordinary least squares models in analyzing repeated measures data

Purpose: 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. Methods: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. Results: 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. Conclusions: 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.