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

Considers the analysis of longitudinal data by means of the autogressive or simplex model. The finding by D. Rogosa and J. B. Willett that the quasi-Markov simplex model fits a linear growth curve covariance structure is investigated. Under various circumstances the quasi-Markov simplex model is rejected. The procedure is reversed by fitting the linear growth curve to quasi-Markov simplex covariance structure. The linear growth curve, like the quasi-Markov simplex, is not always rejected even though the model is formally incorrect. A quasi-Markov simplex model with structured means is presented. 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. The authors argue that this assumption should be tested and show that the hierarchical Chi-2 test can be used to this end.