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. 2016 Sep:41:71-90.
doi: 10.1016/j.dr.2016.06.004. Epub 2016 Jun 29.

Measurement Invariance Conventions and Reporting: The State of the Art and Future Directions for Psychological Research

Diane L Putnick  1 , Marc H Bornstein  1
Affiliations

Measurement Invariance Conventions and Reporting: The State of the Art and Future Directions for Psychological Research

Diane L Putnick et al. Dev Rev. 2016 Sep.

Abstract

Measurement invariance assesses the psychometric equivalence of a construct across groups or across time. Measurement noninvariance suggests that a construct has a different structure or meaning to different groups or on different measurement occasions in the same group, and so the construct cannot be meaningfully tested or construed across groups or across time. Hence, prior to testing mean differences across groups or measurement occasions (e.g., boys and girls, pretest and posttest), or differential relations of the construct across groups, it is essential to assess the invariance of the construct. Conventions and reporting on measurement invariance are still in flux, and researchers are often left with limited understanding and inconsistent advice. Measurement invariance is tested and established in different steps. This report surveys the state of measurement invariance testing and reporting, and details the results of a literature review of studies that tested invariance. Most tests of measurement invariance include configural, metric, and scalar steps; a residual invariance step is reported for fewer tests. Alternative fit indices (AFIs) are reported as model fit criteria for the vast majority of tests; χ2 is reported as the single index in a minority of invariance tests. Reporting AFIs is associated with higher levels of achieved invariance. Partial invariance is reported for about one-third of tests. In general, sample size, number of groups compared, and model size are unrelated to the level of invariance achieved. Implications for the future of measurement invariance testing, reporting, and best practices are discussed.

Keywords: Comparative psychology; confirmatory factor analysis; measurement invariance; multiple-group analysis; structural equation modeling.

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Figures

Figure 1
Figure 1
A simulated confirmatory factor analysis model of parenting warmth and control. Note. In measurement invariance tests, all models are fit to Chinese and United States groups and parameters are constrained to be equal across the groups. For the invariance models depicted in C, E, and G, the bolded parameters are the focal constraints, which are set to be equivalent in the two groups. For the noninvariance models depicted in B, D, F, and H, there is a path or constraint, represented by a dashed line, that applies only to one group (compared to the base invariance model in A, C, E, and G, respectively, which applies to the other group).
See this image and copyright information in PMC

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