Cited by 4,369Psychometric Methodologies and TestingEducational Assessment and PedagogyPsychological Testing and Assessment

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

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Putnick, Diane L., Bornstein, Marc H.·2016·Developmental Review

DOI 10.1016/j.dr.2016.06.004PMC PMC5145197

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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; 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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“This variation may be attributed to the fact that these studies were conducted over the last several decades, during which understanding (e.g., Putnick & Bornstein, 2016 ) and methodological checklists (e.g., van de Schoot et al., 2012 ) for testing for invariance evolved significantly.”
Background
Measurement invariance of assessments of depression (PHQ-9) and anxiety (GAD-7) across sex, strata and linguistic backgrounds in a European-wide sample of patients after Traumatic Brain Injury
Teymoori, A., Real, R. G. L., Gorbunova, A., Haghish, E. F., Anđelić, N., Wilson, L., Asendorf, T., Menon, D. K., & von Steinbüchel, N. (2019) · Journal of Affective Disorders · doi:10.1016/j.jad.2019.10.035 · Cited by 83
Fortune favours the digitally mature: the impact of digital maturity on the organisational resilience of SME retailers during COVID-19
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Conceptualizing and Measuring Trust, Mistrust, and Distrust: Implications for Advancing Health Equity and Building Trustworthiness
Richmond, J., Anderson, A., Cunningham‐Erves, J., Ozawa, S., & Wilkins, C. H. (2023) · Annual Review of Public Health · doi:10.1146/annurev-publhealth-061022-044737 · Cited by 81
The impact of digital media on children’s intelligence while controlling for genetic differences in cognition and socioeconomic background
Sauce, B., Liebherr, M., Judd, N., & Klingberg, T. (2022) · Scientific Reports · doi:10.1038/s41598-022-11341-2 · Cited by 74
Training spatial cognition enhances mathematical learning in a randomized study of 17,000 children
Judd, N., & Klingberg, T. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01118-4 · Cited by 92
We need to change how we compute RMSEA for nested model comparisons in structural equation modeling.
Savalei, V., Brace, J. C., & Fouladi, R. T. (2023) · Psychological Methods · doi:10.1037/met0000537 · Cited by 95
Effect of Foster Care Intervention on Trajectories of General and Specific Psychopathology Among Children With Histories of Institutional Rearing: A Randomized Clinical Trial
Wade, M., Fox, N. A., Zeanah, C. H., & Nelson, C. A. (2018) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2018.2556 · Cited by 74
Understanding cross-cultural differences in affective teacher-student relationships: A comparison between Dutch and Chinese primary school teachers and students
Chen, M., Zee, M., Koomen, H. M. Y., & Roorda, D. L. (2019) · Journal of School Psychology · doi:10.1016/j.jsp.2019.07.011 · Cited by 77
“Third, as suggested by both Chen (2008) and Putnick and Bornstein (2016), we compared the mean differences (research question 2) revealed in the models with and without imposing equality constraints on non-invariant items.”
Prolonged grief disorder in DSM-5-TR: Early predictors and longitudinal measurement invariance
Boelen, P. A., & Lenferink, L. I. M. (2021) · Australian & New Zealand Journal of Psychiatry · doi:10.1177/00048674211025728 · Cited by 88
“A difference in comparative fit index (CFI) value ⩽ 0.01 and a non-significant chi-square difference test ( p > 0.05) demonstrate invariance for the more constrained model (Putnick and Bornstein, 2016).”
MethodInfluential
Reducing personal clothing consumption: A cross-cultural validation of the comprehensive action determination model
Joanes, T., Gwozdz, W., & Klöckner, C. A. (2020) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2020.101396 · Cited by 85
Synthesising psychometric evidence for the Climate Anxiety Scale and Hogg Eco-Anxiety Scale
Hogg, T. L., Stanley, S. K., & O’Brien, L. V. (2023) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2023.102003 · Cited by 79
Permutation randomization methods for testing measurement equivalence and detecting differential item functioning in multiple-group confirmatory factor analysis.
Jorgensen, T. D., Kite, B. A., Chen, P., & Short, S. D. (2017) · Psychological Methods · doi:10.1037/met0000152 · Cited by 75
“…were only meant to be rules of thumb (Cheung & Rensvold, 2002; Hu & Bentler, 1999), applied researchers may be inclined to treat cutoffs as critical values (Chen, 2007; Putnick & Bornstein, 2016), effectively treating a descriptive index of (change in) model fit as though it were a test statistic.”
BackgroundMethodInfluential
Mental Health of Refugee and Non-refugee Migrant Young People in European Secondary Education: The Role of Family Separation, Daily Material Stress and Perceived Discrimination in Resettlement
Spaas, C., Verelst, A., Devlieger, I., Aalto, S., Andersen, A. J., Durbeej, N., Hilden, P. K., Kankaanpää, R., Primdahl, N. L., Opaas, M., et al. (2021) · Journal of Youth and Adolescence · doi:10.1007/s10964-021-01515-y · Cited by 100
Examining the impact of emotional intelligence on career adaptability: A two-wave cross-lagged study
Parmentier, M., Pirsoul, T., & Nils, F. (2019) · Personality and Individual Differences · doi:10.1016/j.paid.2019.05.052 · Cited by 101
Measuring Electronic Health Literacy: Development, Validation, and Test of Measurement Invariance of a Revised German Version of the eHealth Literacy Scale
Marsall, M., Engelmann, G., Skoda, E., Teufel, M., & Bäuerle, A. (2021) · Journal of Medical Internet Research · doi:10.2196/28252 · Cited by 74
“We applied a cutoff criterion of a difference of CFI ( Δ CFI) of 0.01 as it is proposed as appropriate to assume invariance between two models [75,76].”
Influential
The Necessity of Testing Measurement Invariance in Cross-Cultural Research: Potential Bias in Cross-Cultural Comparisons With Individualism– Collectivism Self-Report Scales
Lacko, D., Čeněk, J., Točík, J., Avsec, A., Đorđević, V., Genc, A., Haka, F., Šakotić-Kurbalija, J., Mohorić, T., Neziri, I., et al. (2022) · Cross-Cultural Research · doi:10.1177/10693971211068971 · Cited by 89
“Measurement invariance can only be assessed by psychometric means (Matsumoto & Yoo, 2006; Putnick & Bornstein, 2016) and naturally stems from the cross-cultural equivalence described above, simultaneously providing statistical evidence for the degree of equivalence.”
BackgroundMethodInfluential
Acceptance and Commitment Therapy Processes and Mediation: Challenges and How to Address Them
Arch, J. J., Fishbein, J. N., Finkelstein, L. B., & Luoma, J. B. (2023) · Behavior Therapy · doi:10.1016/j.beth.2022.07.005 · Cited by 72
Life skills development in physical education: A self-determination theory-based investigation across the school term
Cronin, L., Marchant, D., Johnson, L., Huntley, E., Kosteli, M. C., Varga, J., & Ellison, P. (2020) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2020.101711 · Cited by 99
Getting a deeper understanding of mindfulness in the context of eating behavior: Development and validation of the Mindful Eating Inventory
Peitz, D., Schulze, J., & Warschburger, P. (2020) · Appetite · doi:10.1016/j.appet.2020.105039 · Cited by 82
Investigation of the Impact of School Climate and Teachers’ Self-Efficacy on Job Satisfaction: A Cross-Cultural Approach
Katsantonis, I. (2019) · European Journal of Investigation in Health Psychology and Education · doi:10.3390/ejihpe10010011 · Cited by 82
What explains the degree of internationalization of early-stage entrepreneurial firms? A multilevel study on the joint effects of entrepreneurial self-efficacy, opportunity-motivated entrepreneurship, and home-country institutions
Yang, M. M.-H., Li, T., & Wang, Y. (2020) · Journal of World Business · doi:10.1016/j.jwb.2020.101114 · Cited by 79
Age Inclusive Human Resource Practices, Age Diversity Climate, and Work Ability: Exploring Between- and Within-Person Indirect Effects
Rudolph, C. W., & Zacher, H. (2020) · Work Aging and Retirement · doi:10.1093/workar/waaa008 · Cited by 86
Psychological intimate partner violence against women in the European Union: a cross-national invariance study
Martín-Fernández, M., Gracia, E., & Lila, M. (2019) · BMC Public Health · doi:10.1186/s12889-019-7998-0 · Cited by 88
“This is one of the main strengths of this study, since it allowed us to conduct a latent means analysis to compare the factor means of each country, a procedure that unlike computing the raw prevalence, takes into account the latent structure of the construct and the weight of each item to assess it [28, 29].”
Method
Developmental Assets framework revisited: Confirmatory analysis and invariance testing to create a new generation of assets measures for applied research
Syvertsen, A. K., Scales, P., & Toomey, R. B. (2019) · Applied Developmental Science · doi:10.1080/10888691.2019.1613155 · Cited by 58
“Model fit was assessed using a standard set of relative and absolute fit indices (Brown, 2015; Little, 2013; Putnick & Bornstein, 2016).”
Method
Dimensionality and reliability of a screening instrument for students at-risk of dropping out from Higher Education
Casanova, J. R., Gomes, C. M. A., Bernardo, A. B., Núñez, J. C., & Almeida, L. S. (2020) · Studies In Educational Evaluation · doi:10.1016/j.stueduc.2020.100957 · Cited by 81
Dyadic measurement invariance and its importance for replicability in romantic relationship science
Sakaluk, J. K., Fisher, A. N., & Kilshaw, R. E. (2021) · Personal Relationships · doi:10.1111/pere.12341 · Cited by 74
Facing the dropout crisis among PhD candidates: the role of supervisor support in emotional well-being and intended doctoral persistence among men and women
Wollast, R., Aelenei, C., Chevalère, J., Van der Linden, N., Galand, B., Azzi, A., Frenay, M., & Klein, O. (2023) · Studies in Higher Education · doi:10.1080/03075079.2023.2172151 · Cited by 68
“Finally, a strict invariance model is tested in which factor loadings, intercepts and residuals are constrained to be equal across groups (Putnick and Bornstein 2016).”
Method
Safety self-efficacy and internal locus of control as mediators of safety motivation – Randomized controlled trial (RCT) study
Nykänen, M., Salmela‐Aro, K., Tolvanen, A. J., & Vuori, J. (2019) · Safety Science · doi:10.1016/j.ssci.2019.04.037 · Cited by 85
Right-wing political orientation, national identification and the acceptance of immigrants and minorities
Verkuyten, M., Kollar, R., Gale, J., & Yogeeswaran, K. (2021) · Personality and Individual Differences · doi:10.1016/j.paid.2021.111217 · Cited by 72
Psychometric properties and measurement invariance of the 7-item General Anxiety Disorder scale (GAD-7) in an Italian coronary heart disease population
Bolgeo, T., Matteo, R. D., Simonelli, N., Molin, A. D., Lusignani, M., Bassola, B., Vellone, E., Maconi, A., & Iovino, P. (2023) · Journal of Affective Disorders · doi:10.1016/j.jad.2023.04.140 · Cited by 75
More alike than different: Profiles of high-income and low-income rooftop solar adopters in the United States
Wolske, K. S. (2020) · Energy Research & Social Science · doi:10.1016/j.erss.2019.101399 · Cited by 73
Structural validity and invariance of the Feedback Perceptions Questionnaire
Strijbos, J.-W., Pat‐El, R., & Narciss, S. (2021) · Studies In Educational Evaluation · doi:10.1016/j.stueduc.2021.100980 · Cited by 87
“…use the following critical values to assess invariance: -0.01 Δ CFI for metric and scalar invariance and .015 for strict invariance, 0.015 Δ RMSEA for metric and scalar invariance, 0.030 Δ SRMR for metric invariance and 0.015 Δ SRMR for scalar invariance (Putnick & Bornstein, 2016; Chen, 2007).”
BackgroundMethodInfluential
Exploring the Dimensions of Smartphone Distraction: Development, Validation, Measurement Invariance, and Latent Mean Differences of the Smartphone Distraction Scale (SDS)
Throuvala, M. A., Pontes, H. M., Tsaousis, I., Griffiths, M. D., Rennoldson, M., & Kuss, D. J. (2021) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2021.642634 · Cited by 94
“002), thus supporting metric invariance implying equal salience of factors for both male and female students (Table 4) (228).”
Measuring Growth Mindset
Rammstedt, B., Grüning, D. J., & Lechner, C. M. (2022) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000735 · Cited by 100
Sustainable food literacy: A measure to promote sustainable diet practices
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Has COVID-19 changed our loyalty towards public transport? Understanding the moderating role of the pandemic in the relationship between service quality, customer satisfaction and loyalty
Esmailpour, J., Aghabayk, K., Aghajanzadeh, M., & Gruyter, C. D. (2022) · Transportation Research Part A: Policy and Practice · doi:10.1016/j.tra.2022.05.023 · Cited by 65
Essential Validation Criteria for Rigorous Covariance‐Based Structural Equation Modelling
Gaskin, J. E., Lowry, P. B., Rosengren, W., & Fife, P. C. (2025) · Information Systems Journal · doi:10.1111/isj.12598 · Cited by 112
Der Glaube an Big Data
Lünich, M. (2022) · Springer eBooks · doi:10.1007/978-3-658-36368-0 · Cited by 68

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.
ORCID: Putnick, Diane L.
Bornstein, Marc H.
Venue: Developmental Review
Publisher: Elsevier BV
Published: 2016-09
Volume: 41
Pages: 71-90
ISSN: 0273-2297 (ISSN-L)
DOI: 10.1016/j.dr.2016.06.004
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
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
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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Measurement invariance conventions and reporting: The state of the art and future directions for psychological research

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