A Didactic Investigation of Perfect Fit in Second-Order Confirmatory Factor Analysis: Exploratory Structural Equation Modeling and Bayesian Approaches
Larry R. Price · SM Journal of Biometrics & Biostatistics · 2017
Confirmatory Factor Analysis (CFA) plays an integral role in establishing evidence for the validity of test scores.This study provides a didactic strategy on the systematic investigation of perfect model-data fit in CFA.Specific steps presented include (a) investigating the impact of sample size on model fit indices, power and Type II error, (b) demonstration of how Muthén and Asparouhov's (2012) [1] ESEM approach is used to aid in evaluating the second-order factor model for simple structure, and (c) illustrating the tenability of Bayesian Structural Equation Modeling (BSEM) in resolving a non-positive definite matrix solution and in capturing the relationships between the measurement and latent variable parts of the second-order model in a way that provides an optimal tradeoff between simple structure and perfect model-data fit.The ESEM hierarchical approach identified loadings contradicting the original factor analytic results.Bayesian second-order CFA revealed that latent regressions were inflated in the original second-order CFA resulting in an in admissible solution due to a non-positive definite latent variable matrix.Respecification of the factor model using BSEM informed by the ESEM analysis eliminated the inadmissible solution and provided unbiased parameter estimates across sample sizes of N=100, 300, 600 and 1000.