Graduation Year

2003

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Measurement and Evaluation

Major Professor

Robert F. Dedrick, Ph.D.

Co-Major Professor

Paul E. Greenbaum, Ph.D.

Committee Member

C. Hendricks Brown, Ph.D.

Committee Member

John Ferron, Ph.D.

Committee Member

Cynthia Parshall, Ph.D.

Keywords

Monte Carlo simulation, structural equation model, noncentral chisquare distribution, longitudinal design, sample size determination

Abstract

This study employed Monte Carlo simulation to investigate the ability of the growth mixture model (GMM) to correctly identify models based on a "true" two-class pseudo-population from alternative models consisting of "false" one- and three-latent trajectory classes. This ability was assessed in terms of statistical power, defined as the proportion of replications that correctly identified the two-class model as having optimal fit to the data compared to the one-class model, and accuracy, which was defined as the proportion of replications that correctly identified the two-class model over both one- and three-class models. Estimates of power and accuracy were adjusted by empirically derived critical values to reflect nominal Type I error rates of a = .05. Six experimental conditions were examined: (a) standardized between-class differences in growth parameters, (b) percentage of total variance explained by growth parameters, (c) correlation between intercepts and slopes, (d) sample size, (e) number of repeated measures, and (f) planned missingness. Estimates of statistical power and accuracy were related to a measure of the degree of separation and distinction between latent trajectory classes (λ2 ), which approximated a chi-square based noncentrality parameter. Model selection relied on four criteria: (a) the Bayesian information criterion (BIC), (b) the sample-size adjusted BIC (ABIC), (c) the Akaike information criterion (AIC), and (d) the likelihood ratio test (LRT). Results showed that power and accuracy of the GMM to correctly enumerate latent trajectory classes were positively related to greater between-class separation, greater proportion of total variance explained by growth parameters, larger sample sizes, greater numbers of repeated measures, and larger negative correlations between intercepts and slopes; and inversely related to greater proportions of missing data. Results of the Monte Carlo simulations were field tested using specific design and population characteristics from an evaluation of a longitudinal demonstration project. This test compared estimates of power and accuracy generated via Monte Carlo simulation to estimates predicted from a regression of derived λ2 values. Results of this motivating example indicated that knowledge of λ2 can be useful in the two-class case for predicting power and accuracy without extensive Monte Carlo simulations.

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