Comparison of Maximum Likelihood, Bayesian, Partial Least Squares, and Generalized Structured Component Analysis Methods for Estimation of Structural Equation Models with Small Samples: An Exploratory Study
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Structural equation modeling (SEM) is a common analytic approach for dealing with complex systems of information. Despite its power and flexibility (Zhu, Walter, Rosenbaum, Russell, & Raina, 2006), traditional SEM methods require large samples in general, and even larger samples for estimating complex models. For educational researchers, large samples are often difficult and even impossible to obtain.
The purpose of the present study was to evaluate the performance of traditional (i.e., maximum likelihood) and non-traditional (i.e., Bayesian estimation, partial least squares, generalized structured component analysis) methods of estimation available to modern researchers for estimating structural equation models. Specifically, this research focuses on estimation of the structural relationships of a path model with a small sample and multiple groups. The analytical process for this project was comprised of the following steps: 1) a theoretical model was simplified, 2) the revised model was estimated for the multiple subgroups existing within the data, and 3) alternative estimation procedures were used to evaluate the final model for the overall group and each subgroup.
It was found Bayesian estimation, partial least squares, and generalized structured component analysis performed equally well relative to maximum likelihood, as these methods produced roughly equal model fit values. However, with respect to the relative performance of the estimation methods in the recovery of parameter estimates, few consistent patterns of results emerged. Together, these findings imply that more research is necessary to better understand the conditions under which these estimation methods might be expected to produce biased estimates.
Adviser: James A. Bovaird