Measurement invariance conventions and reporting: The state of the art and future directions for psychological research

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.

Assessing decision regret in caregivers of deceased German people with cancer—A psychometric validation of the Decision Regret Scale for Caregivers

“…To evaluate across‐group equivalence of the parameters, we tested for measurement invariance employing multi‐group confirmatory factor analyses across gender (male vs. female), age groups (under 50 years old vs. 50 years or older) and closeness of relationship (spouse/first‐degree relative vs. other; Appendix ) . In sum, we concluded that the respondents from different groups with same the latent level of decision regret responded similarly to a particular item of the DRS‐C.…”

Long-Term Stability of Language Performance in Very Preterm, Moderate-Late Preterm, and Term Children

“…Standardized path coefficients were interpreted with respect to Cohen’s 8 estimates of small (.10), medium (.30), and large (.50) effects. Following a test of the stability of language performance in the full sample, we established at least partial metric and scalar invariance (i.e., constraining the loadings of observed variables on factors and first-order factors on second-order factors, and constraining intercepts of observed and latent first-order factors across groups) 9,10 to make sure the factors had the same meaning in the very preterm, moderate-late preterm, and term groups. Then we computed two additional multiple-group models, constraining the structural paths to be equal across the three gestation groups in the first model and releasing these paths in the second model to determine whether the stability model fit equally well for very preterm, moderate-late preterm, and term children.…”

Effort-reward imbalance and work-home interference: a two-wave study among European male nurses

“…In case the measurement instrument does not show at least partial metric equivalence, cross-country differences in relationships need to be interpreted with caution (e.g. Putnick & Bornstein, 2016). Results showed configural measurement invariance.…”

“…Marsh, Wen, & Hau, 2004). The goodness-of-fit of the models was evaluated using multiple fit indices (cf., Browne & Cudeck, 1992;Putnick & Bornstein, 2016): the Chi 2 goodness-of-fit statistic, the Tucker Lewis Index (TLI), the Comparative Fit Index (CFI) and the Root Mean Square Error of Approximation (RMSEA). TLI and CFI close to or larger than .95 in combination with RMSEA ≤ .05 indicate good fit.…”