Two Aspects of the Simplex Model: Goodness of Fit to Linear Growth Curve Structures and the Analysis of Mean Trends

Abstract

This article has two objectives. The first is to investigate in greater detail the finding of Rogosa and Willett that the quasi-Markov simplex model fits a linear growth curve covariance structure. It is found that under various circumstances the quasi-Markov simplex model is rejected. Furthermore, the procedure is reversed by fitting the linear growth curve to quasi-Markov simplex covariance structure. It is found that the linear growth curve, like the quasi-Markov simplex, is not always rejected even though the model is formally incorrect. The second objective of this article is to present a quasi-Markov simplex model with structured means. This model, like the linear growth curve model with structured means, is based on the assumption that the variation in means and individual differences are attributable to the same causal agents. We argue that this assumption should be tested explicitly. An example is given.