The Role of Model Complexity in the Evaluation of Structural Equation Models

This dissertation represents an investigation into the role of model complexity in structural equation modeling (SEM) and how traditional notions of model fit, which do not typically consider complexity, are inadequate for summarizing the success or failure of a model. Model fit is traditionally summarized in an index which communicates the agreement between a given model and a particular data set. However, demonstrating that a given model could have generated a given data set is not sufficient to show that it is a good model. Because complexity partially determines the ability of a model to fit data, model complexity should not be ignored when evaluating model fit. The importance of model complexity is examined in the SEM context by simulating correlation matrices and applying a series of models which differ in complexity. First, it is shown that models differing in the number of free parameters can fit the same random data differentially well by a simple criterion of good fit. Second, models with the same number of free parameters, but which differ in functional form, are found to fit the same data differentially well. Third, it is found that restrictions placed on parameter range have an impact on model complexity. Because traditional fit indices usually correct for model complexity due only to the number of free parameters, these findings have important implications for how models are assessed and compared in the SEM paradigm.