Latent Growth Curve and Repeated Measures ANOVA Contrasts: What the Models are Telling You

The relationship between the latent growth curve and repeated measures ANOVA models is often misunderstood. Although a number of investigators have looked into the similarities and differences among these models, a cursory reading of the literature can give the impression that they are very different models. Here we show that each model represents a set of contrasts on the occasion means. We demonstrate that the fixed effects parameters of the estimated basis vector latent growth curve model are merely a transformation of the repeated measures ANOVA fixed effects parameters. We further show that differences in fit in models that estimate the same means structure can be due to the different error covariance structures implied by the model. We show these relationships both algebraically and through using data from a simulation.