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A Comparison of Noniterative Generalized Least Squares and Iterative Maximum Likelihood Estimators When Testing Hypotheses in Random Coefficient Growth Curve Models

Abstract Random coefficient growth curve (RCGC) models play an important role in longitudinal studies where the coefficients are allowed to vary across individual experimental units to account for individual differences. In this study, noniterative estimated generalized least squares (EGLS) estimators are investigated and compared to maximum likelihood estimates (MLE) using Monte Carlo simulations. The main objectives of the study are to find the sample size for which Type I errors are controlled for a fixed number of repeated measures, and to compare the power of fixed effect tests using the two estimation methods. Using the EGLS method, sample sizes as small as 10 subjects per group are sufficient to control the Type I error, with a few exceptions. For less than seven repeated measures and large error variances, 30 subjects per group are needed to maintain the Type I error rate. In comparison, MLE generally provide larger Type I errors but greater power. Similar results are obtained for data missing completely at random.