Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators

• In Event: Structural Equation Modeling With Ordinal/Categorical Data

Abstract

Invariance testing has emerged as a critical component to investigate whether factor structures are equal across populations. However, a paucity of research has compared estimation methods within a measurement invariance framework to determine if research conclusions using maximum likelihood (ML) estimation with continuous indicators generalize to robust ML and weighted least squares means and variance adjusted estimators. Using categorical inidcators, this simulation study addressed this query by investigating 342 conditions. When testing for metric (i.e., factor loadings) and scalar (i.e., intercepts or thresholds) invariance, Δχ2 results revealed that Type I error rates and power varied across estimators and research conditions. Changes in approximate fit indices also varied based on the research conditions, but fewer differences emerged between estimators.

Authors

• Daniel Sass, The University of Texas - San Antonio

• Tom Schmitt

• Herbert W. Marsh, University of Western Sydney