A comparison of structural equation and multidimensional Rasch modeling approaches to Confirmatory Factor Analysis

This paper compares the results of applications of the Multidimensional Random Coefficients Multinomial Logit Model (MRCMLM) to comparable Structural Equation Model (SEM) applications for the purpose of conducting a Confirmatory Factor Analysis (CFA). We review SEM as it is applied to CFA, identify some parallels between the MRCMLM approach to CFA and that utilized in a standard SEM CFA, and illustrate the comparability of MRCMLM and SEM CFA results for three datasets. Results indicate that the two approaches tend to identify similar dimensional models as exhibiting best fit and provide comparable depictions of latent variable correlations, but the two procedures depict the reliability of measures differently.