Specification Search for Identifying the Correct Mean Trajectory in Polynomial Latent Growth Models

Abstract

This study investigated the optimal strategy for model specification search under the latent growth modeling (LGM) framework, specifically on searching for the correct polynomial mean or average growth model when there is no a priori hypothesized model in the absence of theory. In this simulation study, the effectiveness of different starting models on the search of the true mean growth model was investigated in terms of the mean and within-subject variance-covariance (V-C) structure model. The results showed that specifying the most complex (i.e., unstructured) within-subject V-C structure with the use of LRT, ΔAIC, and ΔBIC achieved the highest recovery rate (>85%) of the true mean trajectory. Implications of the findings and limitations are discussed.

Keywords:

• growth curve analysis
• growth models
• latent growth modeling
• model selection
• specification search

Notes

The most complex within-subject V-C matrix is specified as the unstructured (UN) structure in which all the unique elements/parameters are estimated while the between-subject V-C matrix is specified as a null matrix (i.e., all elements are fixed to zero and no parameter is estimated) for identification purpose.

Instead of the seventh-order polynomial model, we used the sixth-order polynomial model as the most complex mean model given that the seventh-order polynomial model resulted in serious nonconvergence issue.

For identification purpose, the covariances between cubic growth term were constrained to be zero for four- wave data. For the same reason, the covariances among fourth- and higher-order growth factors for eight-wave data were constrained to be zero given that these parameters were zeros under the true (quadratic) model.

Additional information

Notes on contributors

Minjung Kim

Minjung Kim is a Postdoc Fellow in the Department of Psychology at the University of South Carolina. Her primary research interests include latent variable modeling (e.g., regression mixture models, growth mixture models) and longitudinal data analysis using multilevel modeling and latent growth modeling.

Oi-Man Kwok

Oi-Man Kwok is a professor at the Department of Educational Psychology, Texas A&M University. His main research interests include modeling longitudinal data using structural equation models and multilevel models.

Myeongsun Yoon

Myeongsun Yoon is an assistant professor in the Department of Educational Psychology at Texas A&M University. Her research interests include measurement bias in psychological scales and other measurement issues in confirmatory factor analysis and item response theory.

Victor Willson

Victor L. Willson, Ph.D., received his doctorate from the University of Colorado-Boulder in 1973 under the direction of Dr. Gene V Glass. Their coauthored book, Design and Analysis of Time Series Experiments, 1975, was reprinted as a classic text in the 20th century in the social sciences. Dr. Willson is currently Professor of Educational Psychology and Head, Department of Educational Psychology, at Texas A&M University and Douglas J. Palmer Chair of Educational Psychology. He is a past president of the Southwest Educational Research Association.

Mark H. C. Lai

Mark H. C. Lai is a Ph.D. candidate at the Department of Educational Psychology, Texas A&M University. His research interests are effect size measures in multilevel modeling and evaluating measurement invariance using structural equation modeling.