Evaluating model fit with ordered categorical data within a measurement invariance framework : a comparison of estimators

Daniel A. Sass, Thomas A. Schmitt, Herbert W. Marsh

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A paucity of research has compared estimation methods within a measurement invariance (MI) framework and determined if research conclusions using normal-theory maximum likelihood (ML) generalizes to the robust ML (MLR) and weighted least squares means and variance adjusted (WLSMV) estimators. Using ordered categorical data, this simulation study aimed to address these queries by investigating 342 conditions. When testing for metric and scalar invariance, Δχ2 results revealed that Type I error rates varied across estimators (ML, MLR, and WLSMV) with symmetric and asymmetric data. The Δχ2 power varied substantially based on the estimator selected, type of noninvariant indicator, number of noninvariant indicators, and sample size. Although some the changes in approximate fit indexes (ΔAFI) are relatively sample size independent, researchers who use the ΔAFI with WLSMV should use caution, as these statistics do not perform well with misspecified models. As a supplemental analysis, our results evaluate and suggest cutoff values based on previous research.
    Original languageEnglish
    Pages (from-to)167-180
    Number of pages14
    JournalStructural Equation Modeling
    Volume21
    Issue number2
    DOIs
    Publication statusPublished - 2014

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