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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
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“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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InfluentialKouhsari, M., Huang, X., & Wang, C. (2023) · Cambridge Journal of Education · doi:10.1080/0305764x.2023.2255565 · Cited by 29
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Identifying neuropsychological predictors of drawing skills in elementary school children
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“…of correlations or means for latent variables that are not configurally invariant would be exceptionally difficult to interpret (Little, 2013; Putnick & Bornstein, 2016; Vandenberg & Lance, 2000), and instead, would harken to potentially fundamental differences in mental construction of the…”
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“A key assumption, upon which the validity of any PROM data depends, is measurement invariance.(5) Measurement invariance requires that the concept being measured by a”
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“The mismatch between RMSEA and SRMR as indicators of configural fit can likely be explained by the fact that SRMR increases and RMSEA decreases with the number of degrees of freedom (Putnick & Bornstein, 2016).”
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“…to scales needing to have construct validity to ensure they are measuring what they intend to measure, researchers also want to be confident that their scales are cross-cultural valid and that there is measurement invariance across samples (Meitinger et al., 2020 Putnick & Bornstein, 2016;).”
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The Merits of Goal Support as a Self-Control Strategy
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A cross-cultural comparison of expectations in romantic relationships: India and the United States
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“In the third step, scalar invariance, researchers tested whether the “mean differences in the latent construct capture all mean differences in the shared variance of the items” (Putnick & Bornstein, 2016, p. 76).”
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“Other changes in goodnessof-fit criteria are also used when comparing nested MI models, such as ΔCFI, ΔRMSEA, and ΔSRMR, particularly with large samples when differences or changes in χ2 are statistically significant (Putnick and Bornstein, 2016).”
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“Factor structure of psychopathy In this study, we rely on confirmatory factor analysis of the PCL-R which is, like the IRT approach by Bolt et al. (2004), a suitable approach to test for measurement invariance across gender (Putnick & Bornstein, 2016).”
Gfrörer, T., Stoll, G., Rieger, S., Trautwein, U., & Nagengast, B. (2021) · European Journal of Personality · doi:10.1177/08902070211035630 · Cited by 18
“Aiming for partial invariance is a suitable approach when invariance cannot be achieved on all items (Putnick & Bornstein, 2016).”
BackgroundMethodSupporting Undergraduate Biology Students’ Academic Success: Comparing Two Workshop Interventions
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“We considered three measurement invariance steps: 1) configural, equivalence of model form; 2) metric, equivalence of factor loadings; and 3) scalar, equivalence of item intercepts (Putnick and Bornstein, 2016; Wang and Wang, 2019).”
MethodMeier, Y., Schäwel, J., & Krämer, N. C. (2021) · Studies in Communication and Media · doi:10.5771/2192-4007-2021-3-283 · Cited by 17
The LIVES Daily Hassles Scale and Its Relation to Life Satisfaction
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“We considered noninvariance when model differences exceeded the recommended cutoff values (significant Δχ2, ΔCFI > .01, and ΔRMSEA > .015, lowest BIC, see Cheung & Rensvold, 2002; Putnick & Bornstein, 2016).”
MethodValidation and measurement invariance of the Occupational Depression Inventory in South Africa
Hill, C., Beer, L. T. D., & Bianchi, R. (2021) · PLoS ONE · doi:10.1371/journal.pone.0261271 · Cited by 21
Franco, L. R., Juarros‐Basterretxea, J., Paíno-Quesada, S., Herrero, J., & Rodríguez‐Díaz, F. J. (2021) · International Journal of Clinical and Health Psychology · doi:10.1016/j.ijchp.2021.100276 · Cited by 20
Hazzard, V. M., Schaefer, L. M., Thompson, J. K., Rodgers, R. F., & Frederick, D. A. (2022) · Body Image · doi:10.1016/j.bodyim.2022.01.004 · Cited by 28
Janke, S. (2022) · Learning and Individual Differences · doi:10.1016/j.lindif.2022.102158 · Cited by 23
The Development of a Podcast Motivations Scale for Taiwan
Chou, S., Ma, W., & Britt, R. K. (2022) · Journal of Radio & Audio Media · doi:10.1080/19376529.2022.2044818 · Cited by 23
“Measurement invariance assesses the psychometric equivalence of a construct across groups or time to demonstrate that a construct has the same meaning to those groups or across repeated measurements (Putnick & Bornstein, 2016).”
BackgroundMethodInfluentialStabilnost i/ili promjene? Povjerenje u institucije u Hrvatskoj od 1999. do 2020.
Bovan, K., & Baketa, N. (2022) · Revija za sociologiju · doi:10.5613/rzs.52.1.0315 · Cited by 29
Testing the Invariance of the Metacognitive Monitoring Test
Gomes, C. M. A., de Araujo, J., & Castillo-Díaz, M. A. (2021) · Psico-USF · doi:10.1590/1413-82712021260407 · Cited by 22
Reynolds, K., Khorramdel, L., & von Davier, M. (2022) · Studies In Educational Evaluation · doi:10.1016/j.stueduc.2022.101169 · Cited by 20
Functionality of Apps for People with Autism: Comparison between Educators from Florence and Granada
Montes, C. D. P. G., Fuentes, A. R., Cara, M. J. C., & Capperucci, D. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19127019 · Cited by 20
“In the methodological dimension, the invariance of measurement of the instrument in the two languages needs to be examined, following the proposal by [48].”
BackgroundVogelsmeier, L. V. D. E., Vermunt, J. K., & Roover, K. D. (2022) · Behavior Research Methods · doi:10.3758/s13428-022-01898-1 · Cited by 19
“This implies that strict invariance is not necessary for meaningfully comparing latent covariances or means (Putnick & Bornstein, 2016; Van-denberg & Lance, 2000).”
BackgroundEmotion regulation among Chinese and German children and adolescents: a binational comparative study
Teuber, Z., Schreiber, S., Rueth, J., & Lohaus, A. (2022) · Current Psychology · doi:10.1007/s12144-022-03578-x · Cited by 22
“As pointed out by Putnick and Bornstein (2016), full measurement invariance is often not supported in empirical studies, and as a consequence it has been common practice to accept some violations of measurement invariance by releasing constraints on some parameters such as factor loadings or item…”
Nagle, C. (2022) · Research Methods in Applied Linguistics · doi:10.1016/j.rmal.2022.100033 · Cited by 22
Pratt, J. M., Stewart, J. L., Reisner, B. A., Bentley, A. K., Lin, S., Smith, S. R., & Raker, J. R. (2022) · Chemistry Education Research and Practice · doi:10.1039/d2rp00199c · Cited by 27
Olaru, G., Stieger, M., Rüegger, D., Kowatsch, T., Flückiger, C., Roberts, B. W., & Allemand, M. (2022) · European Journal of Personality · doi:10.1177/08902070221145088 · Cited by 31
“This can be particularly interesting to judge how the traits are affected by the intervention (K¨onen & Karbach, 2021; Putnick & Bornstein, 2016).”
BackgroundDevelopment and validation of the Trust in Multidimensional Healthcare Systems Scale (TIMHSS)
Meyer, S. B., Brown, P. R., Calnan, M., Ward, P., Little, J., Betini, G. S., Perlman, C. M., Burns, K. E., & Filice, E. (2024) · International Journal for Equity in Health · doi:10.1186/s12939-024-02162-y · Cited by 29
“Based on previously established conventions for establishing measurement invariance [67], configural, [63] [Q25] Have you changed physicians in the past or sought a second opinion due to concerns about care?”
MethodSewell, M. N., Yoon, H. J., Lechner, C. M., Napolitano, C. M., Rammstedt, B., Roberts, B. W., & Soto, C. (2024) · Assessment (Odessa, Fla.) · doi:10.1177/10731911241256434 · Cited by 23
“…groups, metric invariance indicates that each item contributes similarly to the latent factor across groups, and scalar invariance indicates that mean differences in the latent SEB skill facets and domains capture all mean differences in the shared variance of the items (Putnick & Bornstein, 2016).”
Jung, E., & Yoon, M. (2016) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2016.1251845 · Cited by 20
“…comparisons of observed scores on measured variables, the establishment of measurement invariance beforehand has been seriously valued and increasingly tested over the last two decades (Putnick & Bornstein, 2016; Schmitt & Kuljanin, 2008; Steenkamp & Baumgartner, 1998; Vandenberg & Lance, 2000).”
BackgroundPsychometric properties of a Cyberbullying Inventory for university students
Tanrıkulu, İ., & Erdur‐Baker, Ö. (2020) · British Journal of Guidance and Counselling · doi:10.1080/03069885.2020.1775174 · Cited by 23
“For example, Putnick and Bornstein (2016) found that the characteristics of the sample and the tested model are important factors impacting the measurement invariance test results.”
BackgroundBueno-Pacheco, A., Lima-Castro, S., Árias-Medina, P., Peña-Contreras, E., Aguilar-Sizer, M., & Cabrera-Vélez, M. (2020) · Revista Iberoamericana de Diagnóstico y Evaluación - e Avaliação Psicológica · doi:10.21865/ridep56.3.07 · Cited by 23
“Valores de ΔCFI .01 revelan ajuste absoluto y, por lo tanto, equivalencia entre grupos (Putnick & Bornstein, 2016).”
BackgroundTrends in parental self-efficacy between 1999 and 2014
Glatz, T., & Buchanan, C. M. (2021) · Journal of Family Studies · doi:10.1080/13229400.2021.1906929 · Cited by 32
“In line with recommendations (Little, 2013; Putnick & Bornstein, 2016; van de Schoot et al., 2012), we used a three-step approach to examine measurement invariance between the two samples, including testing for configural, weak, and strong factorial invariance.”
MethodInequality in socio-emotional skills: a cross-cohort comparison
Mason, G., Conti, G., Blundell, R. W., & Attanasio, O. P. (2020) · doi:10.1920/wp.ifs.2020.1120 · Cited by 22
Liu, H., Xiang, W., Wu, D.-H., Zou, Y.-D., Jiang, X.-B., Gao, Z.-Q., You, R.-H., Hu, J., & Liu, J. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.823400 · Cited by 19
Social, emotional, and behavioral skills in students with or without specific learning disabilities
Feraco, T., Pellegrino, G., Casali, N., Carretti, B., & Meneghetti, C. (2024) · Learning and Individual Differences · doi:10.1016/j.lindif.2024.102581 · Cited by 31
Hlynsson, J. I., Skúlason, S., Andersson, G., & Carlbring, P. (2025) · Psychiatric Quarterly · doi:10.1007/s11126-025-10208-9 · Cited by 22
Adaptation and Validation of the Gratitude Questionnaire GQ-6 for the Ecuadorian Context
Lima-Castro, S., Peña-Contreras, E., Aguilar-Sizer, M., Bueno-Pacheco, A., & Árias-Medina, P. (2019) · Revista Avaliação Psicológica · doi:10.15689/ap.2019.1802.15689.03 · Cited by 18
“…invariance (same patterns on fixed and free loadings), metric invariance (equivalence of the item loadings), scalar invariance (equivalence of the intercept) and latent means invariance (since the construct cannot be directly measured) (Putnick and Bornstein, 2016; Van de Schoot et al., 2012).”
BackgroundCross-Cultural Invariance of the Mental Toughness Index among American and Greek Athletes
Stamatis, A., Morgan, G. B., Papadakis, Z., Mougios, V., Bogdanis, G. C., & Spinou, A. (2019) · Current Psychology · doi:10.1007/s12144-019-00532-2 · Cited by 21
“This process of fitting increasingly restrictive models is the recommended process for examining measurement invariance (Brown 2015; Putnick and Bornstein 2016; Vandenberg and Lance 2000; Widaman and Reise 1997).”
MethodSenese, V. P., Miranda, M. C., Lansford, J. E., Bacchini, D., Nasti, C., & Rohner, R. P. (2020) · Journal of Social and Personal Relationships · doi:10.1177/0265407520912339 · Cited by 19
“The MI of the 35-item FIS across genders was analyzed following Vandenberg and Lance (2000) and Putnick and Bornstein (2016).”
MethodCheng, J. W., Mitomo, H., Kamplean, A., & Seo, Y. (2021) · Telecommunications Policy · doi:10.1016/j.telpol.2021.102185 · Cited by 22
Later Life Workplace Index: Validation of an English Version
Finsel, J. S., Wöhrmann, A. M., Wang, M., Wilckens, M. R., & Deller, J. (2021) · Work Aging and Retirement · doi:10.1093/workar/waab029 · Cited by 24
Goel, N. J., Burnette, C. B., Weinstock, M., & Mazzeo, S. E. (2022) · International Journal of Eating Disorders · doi:10.1002/eat.23696 · Cited by 18
Grüning, D. J., & Lechner, C. M. (2022) · Journal of Personality Assessment · doi:10.1080/00223891.2022.2057318 · Cited by 19
“According to the criteria of Chen (2007), Rutkowski and Svetina (2014), and Putnick and Bornstein (2016), all seven tested models reached scalar measurement invariance between the German and the UK sample (i.e., the factor loadings, intercepts, uniquenesses and factor variances were equal across…”
MethodMourão, L., Tavares, S. M. D. O. E. M., & Sandall, H. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.841768 · Cited by 30
“The fit statistics for these two models were good (χ2 = 0.29, df = 2.00, p = 0.086, GFI = 0.999, CFI = 1.000, SRMR = 0.020, and RMSEA = 0.000 and χ2 = 0.07, df = 2.00, p = 0.096, GFI = 1.000, CFI = 1.000, SRMR = 0.011, and RMSEA = 0.000, respectively).”
BackgroundInfluentialDuBay, M. F., Sideris, J. H., & Rouch, E. F. (2022) · Autism Research · doi:10.1002/aur.2783 · Cited by 20
“This suggests that the items in a given factor do not provide the same contribution to that construct between translation versions of the instrument (Putnick & Bornstein, 2016).”
Background
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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