The DOI matches its Crossref record; 75 of the 75 references it cites were found in a registry or an index.
Measurement invariance conventions and reporting: The state of the art and future directions for psychological research
Open accessAbstract
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; χ 2 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.
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“Evidence of invariance was determined based on changes in fit indices: ΔCFI ≤ 0.010 and ΔRMSEA ≤ 0.015 [64, 65].”
From Psychometric validation and measurement invariance of the Health-Promoting Lifestyle Profile II in Honduran university students (2025) · cites this paper as [64]
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“We can therefore conclude that the differences observed between countries are due to variations in prevalence rates, not discrepancies in participants’ interpretation of the instrument (Putnick & Bornstein, 2016; Vandenberg & Lance, 2000).”
From Online Sexual Harassment Perpetration Among Peer Adolescents: A Cross-National and Cross-Gender Study (2025) · cites this paper as Putnick & Bornstein, 2016
In the citing paper
“The metric model (fixed loadings) was better than the configural model (same variables between time points) with a CFI change of 0.005, RMSEA change of 0.006, and SRMR change of − 0.004; following the cutoff criteria suggested by Putnick and Bornstein41.”
From The impact of digital media on children’s intelligence while controlling for genetic differences in cognition and socioeconomic background (2022) · cites this paper as [41]
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Cites
Statistical Power Analysis for the Behavioral Sciences
Muller, K. E., & Cohen, J. (1989) · Technometrics · doi:10.2307/1270020 · Cited by 99,603
Statistical power analysis for the behavioral sciences
Cohen, J. (1990) · Computers Environment and Urban Systems · doi:10.1016/0198-9715(90)90050-4 · Cited by 65,417
Principles and Practice of Structural Equation Modeling
Tabri, N., & Elliott, C. M. (2012) · Canadian Graduate Journal of Sociology and Criminology · doi:10.15353/cgjsc.v1i1.3787 · Cited by 39,094
(1998) · Cited by 36,049
Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance
Cheung, G. W., & Rensvold, R. B. (2002) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0902_5 · Cited by 16,280 · cited 4×
“A uthor M anuscript A uthor M anuscript A uthor M anuscript A uthor M anuscript indices and criteria should be used to judge “practical” differences in model fit between groups (e.g., Chen, 2007; Cheung & Rensvold, 2002).”
BackgroundMethodInfluentialSensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance
Chen, F. F. (2007) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705510701301834 · Cited by 12,217 · cited 9×
“Overall, the Δχ2 was reported for 62.6% of tests, the change in CFI was reported for 73.2% of tests, and the change in another alternative fit index (e.g., ΔRMSEA, ΔTLI, ΔSRMR) was reported for 56.1% of tests.”
BackgroundMethodInfluentialThe file drawer problem and tolerance for null results.
Rosenthal, R. (1979) · Psychological Bulletin · doi:10.1037/0033-2909.86.3.638 · Cited by 9,068 · cited 1×
“Perhaps tests of many groups rarely appear in the literature because fewer researchers study many groups, measurement invariance is not achieved (e.g., the file drawer problem; Rosenthal, 1979), or model complexity causes researchers to shy away from tests with many groups.”
BackgroundVandenberg, R. J., & Lance, C. E. (2000) · Organizational Research Methods · doi:10.1177/109442810031002 · Cited by 7,997 · cited 7×
“Vandenberg and Lance (2000) soon after outlined 8 steps for testing measurement invariance, with the first 5 steps consisting of the main tests of measurement invariance.”
BackgroundMethodInfluentialAssessing Measurement Invariance in Cross‐National Consumer Research
Steenkamp, J. E. M., & Baumgartner, H. (1998) · Journal of Consumer Research · doi:10.1086/209528 · Cited by 4,760 · cited 5×
“Steenkamp and Baumgartner (1998) suggested that ideally more than half of items on a factor should be invariant.”
BackgroundInfluentialMeasurement Invariance, Factor Analysis and Factorial Invariance
Meredith, W. (1993) · Psychometrika · doi:10.1007/bf02294825 · Cited by 4,536 · cited 2×
“) Although a required component for full factorial invariance (Meredith, 1993), testing for residual invariance is not a prerequisite for testing mean differences because the residuals are not part of the latent factor, so invariance”
Background
Research works printed but not linked: 1
- Rensvold, 2001, Testing for metric invariance using structural equation models: solving the standardization problem, Vol. 1, 21
Cited by
Sorted by citations
Susceptibility to misinformation about COVID-19 around the world
Roozenbeek, J., Schneider, C. R., Dryhurst, S., Kerr, J., Freeman, A. L. J., Recchia, G., van der Bles, A. M., & van der Linden, S. (2020) · Royal Society Open Science · doi:10.1098/rsos.201199 · Cited by 1,447
“We thus find support for weak measurement invariance and, in line with Putnick & Bornstein’s [59] recommendation, proceed with the analysis and interpret this as a minor limitation to our study. royalsocietypublishing.org/journal/rsos R.Soc.”
ResultZacher, H., & Rudolph, C. W. (2021) · American Psychologist · doi:10.1037/amp0000702 · Cited by 643
A Primer to (Cross-Cultural) Multi-Group Invariance Testing Possibilities in R
Fischer, R. D., & Karl, J. A. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.01507 · Cited by 396
Tomasik, M. J., Helbling, L. A., & Moser, U. (2021) · International Journal of Psychology · doi:10.1002/ijop.12728 · Cited by 378
“Following Chen (2007); as cited in Putnick & Bornstein, 2016), the criteria we used for assessing invariance were ΔCFI < .01, ΔRMSEA < .015 and ΔSRMR < .030 (for weak invariance only) or ΔSRMR < .015 (for strong and strict invariance).”
MethodPsychometric Properties of the Climate Change Worry Scale
Stewart, A. E. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18020494 · Cited by 286
Metadata
- Authors
- Putnick, D. L., & Bornstein, M. H.
- Affiliations
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (US)
- Corresponding author
- Putnick, Diane L.
- Venue
- Developmental Review
- Publisher
- Elsevier BV
- Published
- 2016-09
- Volume
- 41
- Pages
- 71-90
- ISSN
- 0273-2297 (ISSN-L)
- PMC
- PMC5145197
- OpenAlex
- W2469775770
- Cited by
- 4,369
- References
- 75
- Citations by year
- 2026: 988 · 2025: 736 · 2024: 653 · 2023: 560 · 2022: 520 · 2021: 458 · 2020: 270 · 2019: 128 · 2018: 40 · 2017: 7 · 2016: 2
- FWCI
- 64.55
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Developmental Review (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- NIH
- NICHD
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Education › Educational Assessment and Pedagogy
- Social Sciences › Psychology › Applied Psychology › Psychological Testing and Assessment
- Keywords
- measurement invariance, configural invariance, metric invariance, scalar invariance, partial invariance, cross-group comparison, longitudinal assessment, best practices
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