Measurement Models in Social Work Research: A Data-Based Illustration of Four Confirmatory Factor Models and Their Conceptual Application

Purpose:Confirmatory Factor Analysis (CFA) is a commonly used method to estimate latent factors among a group of observed variables. CFA models provide a valuable tool for social work researchers to examine factor validity, but little attention is given to the conceptual and theoretical implications of various models (i.e., second- and third-order models, correlated vs. uncorrelated models). Evaluating the appropriateness of multiple structural models is a careful balance between theoretical plausibility, parsimony, and quantitative techniques such as statistical tests of difference and fit indices. The purpose of this presentation is to use data to illustrate four different CFA models using four different analytic software packages that explain relationships among latent variables and their conceptual application to measurement in social work research.

Methods: For a data-based illustration of the four models (i.e., single-factor, correlated, second- and bifactor models), we utilized survey data on empathy from 463 students from a large, Southwest university (72% female; average age=22.8 years, SD=6.9 years; 54.4% Caucasian, 24% Latino, 5.6% African Americans). Analyses were performed in Mplus, R, and STATA using the WLSMV estimator as the data were categorical and in EQS 6.1 with an ML estimator on a polychoric correlation matrix (comparable to WLSMV and instead of a Pearson product-moment correlation). Model fit was assessed with conventional fit indices including the model chi-square value (χ2), chi-square statistic per degrees of freedom (χ2/df<3.0), Satorra-Bentler scaled chi-square (SBχ²), the Comparative Fit Index (CFI≥.95), Tucker-Lewis index (TLI≥.95), the Incremental Fit Index (IFI≥.95), the McDonald Fit Index (MFI≤.89), Weighted root-mean-square residual (WRMR≤1.0), and the Root Mean Square Error of Approximation (RMSEA≤.06 to .08 with a 90% confidence interval). Because we were evaluating the fit of multiple models, we used a Satorra-Bentler scaled chi-square difference test (Satorra & Bentler, 2001) and Akaike’s Information Criterion (AIC) to make comparisons between models. 

Results:We present data and theoretical application on following models: (1) a single-factor General Empathy (GE) model; (2) a correlated four-factor model among affective response (AR), self-other awareness (SOA), perspective-taking (PT) and emotion regulation (ER); (3) a higher-order model where AR, SOA, PT and ER comprised the first order factors and second-order GE latent factor; and (4) a bifactor model that included the AR, SOA, PT and ER factors, as well as a GE factor. Results from each model and their conceptual plausibility are presented. Measurement implications from each model are discussed. Syntax for all models in Mplus, R, STATA, and EQS 6.1 programs are provided for reference.

Conclusions: Developing an instrument is an iterative task that requires researchers to evaluate empirical decisions with theoretical plausibility and model parsimony. The purpose of the current study was to demonstrate various structural and theoretical implications of different CFA models through the evaluation and comparison of four alternative models that represent empathy. As familiarity with CFA and structural equation modeling methods grow, social work researchers are encouraged to understand the theory-based implications of measurement models and test alternative models that best represent their data and explain their conceptual application.