A checklist for testing measurement invariance
Abstract
The analysis of measurement invariance of latent constructs is important in research across groups, or across time. By establishing whether factor loadings, intercepts and residual variances are equivalent in a factor model that measures a latent concept, we can assure that comparisons that are made on the latent variable are valid across groups or time. Establishing measurement invariance involves running a set of increasingly constrained structural equation models, and testing whether differences between these models are significant. This paper provides a step-by-step guide to analysing measurement invariance.
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<b>lavaan</b> : An <i>R</i> Package for Structural Equation Modeling
Rosseel, Y. (2012) · Journal of Statistical Software · doi:10.18637/jss.v048.i02 · Cited by 27,955 · see citing works
Simultaneous Factor Analysis in Several Populations
Jöreskog, K. G. (1971) · Psychometrika · doi:10.1007/bf02291366 · Cited by 2,051 · cited 2× · see citing works
“Joreskog ( 1971 ) was the first author to write about the equivalence of factor structures.”
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Putnick, D. L., & Bornstein, M. H. (2016) · Developmental Review · doi:10.1016/j.dr.2016.06.004 · Cited by 4,369 · see citing works
Greenier, V., Derakhshan, A., & Fathi, J. (2021) · System · doi:10.1016/j.system.2020.102446 · Cited by 576 · see citing works
Gender differences in loneliness across the lifespan: a meta-analysis
Maes, M., Qualter, P., Vanhalst, J., Van den Noortgate, W., & Goossens, L. (2019) · European Journal of Personality · doi:10.1002/per.2220 · Cited by 405 · see citing works
Kehr, F., Kowatsch, T., Wentzel, D., & Fleisch, E. (2015) · Information Systems Journal · doi:10.1111/isj.12062 · Cited by 410 · see citing works
Boer, M., Stevens, G. W. J. M., Finkenauer, C., de Looze, M. E., & van den Eijnden, R. J. J. M. (2021) · Computers in Human Behavior · doi:10.1016/j.chb.2020.106645 · Cited by 335 · see citing works
Leung, H., Pakpour, A. H., Strong, C., Lin, Y.-C., Tsai, M.-C., Griffiths, M. D., Lin, C.-Y., & Chen, I.-H. (2020) · Addictive Behaviors · doi:10.1016/j.addbeh.2019.04.027 · Cited by 290 · see citing works
Dicke, T., Parker, P. D., Holzberger, D., Kunina-Habenicht, O., Kunter, M., & Leutner, D. (2015) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2014.11.003 · Cited by 208 · see citing works
Rossi, A., Panzeri, A., Pietrabissa, G., Manzoni, G. M., Castelnuovo, G., & Mannarini, S. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.02177 · Cited by 166 · see citing works
“…an “acceptable” model fit and values below 0.05 indicating a “good” model fit (Steiger and Lind, 1980; Steiger, 1990; Hu and Bentler, 1999; Barrett, 2007; van de Schoot et al., 2012); (C) the comparative fit index (CFI), with values between 0.90 and 0.95 for an “acceptable” fit (Browne and…”
BackgroundMethodInfluentialDevelopment and preliminary validation of the mindfulness inventory for sport.
Thienot, E., Jackson, B., Dimmock, J., Grove, J. R., Bernier, M., & Fournier, J. F. (2014) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2013.10.003 · Cited by 165 · see citing works
Boer, M., Stevens, G., Finkenauer, C., & van den Eijnden, R. (2020) · Child Development · doi:10.1111/cdev.13334 · Cited by 157 · see citing works
“Hyperactivity was thereby sufficiently invariant over time for the purposes of our analyses (Van de Schoot et al., 2012).”
BackgroundLiekefett, L., Christ, O., & Becker, J. C. (2023) · Personality and Social Psychology Bulletin · doi:10.1177/01461672211060965 · Cited by 155 · see citing works
Pelikan, E. R., Korlat, S., Reiter, J., Holzer, J., Mayerhofer, M., Schober, B., Spiel, C., Hamzallari, O., Uka, A., Chen, J., et al. (2021) · PLOS ONE · doi:10.1371/journal.pone.0257346 · Cited by 141 · see citing works
Reis, D., Lehr, D., Heber, E., & Ebert, D. D. (2019) · Assessment · doi:10.1177/1073191117715731 · Cited by 127 · see citing works
Park, C. L., Finkelstein-Fox, L., Russell, B. S., Fendrich, M., Hutchison, M., & Becker, J. (2021) · American Psychologist · doi:10.1037/amp0000813 · Cited by 127 · see citing works
Falkenström, F., Hatcher, R. L., Skjulsvik, T., Larsson, M. H., & Holmqvist, R. (2015) · Psychological Assessment · doi:10.1037/pas0000038 · Cited by 117 · see citing works
Heissel, A., Pietrek, A., Flunger, B., Fydrich, T., Rapp, M. A., Heinzel, S., & Vansteenkiste, M. (2018) · European Journal of Health Psychology · doi:10.1027/2512-8442/a000017 · Cited by 106 · see citing works
Starke, C., & Lünich, M. (2020) · Data & Policy · doi:10.1017/dap.2020.19 · Cited by 107 · see citing works
Lu, S., Hu, S., Guan, Y., Xiao, J., Cai, D., Gao, Z., Sang, Z., Wei, J., Zhang, X., & Margraf, J. (2018) · Frontiers in Psychology · doi:10.3389/fpsyg.2018.02064 · Cited by 102 · see citing works
Pedersen, G., Kvarstein, E. H., & Wilberg, T. (2017) · Personality and Mental Health · doi:10.1002/pmh.1382 · Cited by 90 · see citing works
Grégoire, S., Gagnon, J., Lachance, L., Shankland, R., Dionne, F., Kotsou, I., Monestès, J.-L., Rolffs, J. L., & Rogge, R. D. (2020) · Journal of Contextual Behavioral Science · doi:10.1016/j.jcbs.2020.06.004 · Cited by 85 · see citing works
Smith, K. V., & Ehlers, A. (2020) · Journal of Consulting and Clinical Psychology · doi:10.1037/ccp0000438 · Cited by 73 · see citing works
Fütterer, T., Scherer, R., Scheiter, K., Stürmer, K., & Lachner, A. (2023) · Computers & Education · doi:10.1016/j.compedu.2023.104756 · Cited by 70 · see citing works
Montero-Marín, J., Gaete, J., Demarzo, M., Rodero, B., Lopez, L. C. S., & García-Campayo, J. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.01281 · Cited by 66 · see citing works
Development and validation of the motivations for social media use scale (MSMU) among adolescents
Rodgers, R. F., Mclean, S. A., Gordon, C. S., Slater, A., Marques, M. D., Jarman, H. K., & Paxton, S. J. (2021) · Adolescent Research Review · doi:10.1007/s40894-020-00139-w · Cited by 64 · see citing works
Alt, P., Reim, J., & Walper, S. (2021) · Journal of Research on Adolescence · doi:10.1111/jora.12648 · Cited by 63 · see citing works
Lin, Y.-Y., Rogge, R. D., & Swanson, D. P. (2020) · Journal of Contextual Behavioral Science · doi:10.1016/j.jcbs.2019.11.008 · Cited by 58 · see citing works
Zhu, C., Jiang, Y., Lei, H., Wang, H., & Zhang, C. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e30346 · Cited by 60 · see citing works
Maes, C., Trekels, J., Tylka, T. L., & Vandenbosch, L. (2021) · Body Image · doi:10.1016/j.bodyim.2021.05.004 · Cited by 52 · see citing works
Monacis, L., Griffiths, M. D., Limone, P., Sinatra, M., & Servidio, R. (2020) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph17165738 · Cited by 50 · see citing works
Job seekers' attitudes toward cybervetting: Scale development, validation, and platform comparison
Cook, R., Jones‐Chick, R., Roulin, N., & O'Rourke, K. (2020) · International Journal of Selection and Assessment · doi:10.1111/ijsa.12300 · Cited by 42 · see citing works
Psychological Inflexibility and Child Anxiety.
Simon, E., & Verboon, P. (2016) · Journal of Child and Family Studies · doi:10.1007/s10826-016-0522-6 · Cited by 39 · see citing works
“To test measurement invariance we ran a number of models based on the procedure proposed by van de Schoot, Lugtig, and Hox (Van de Schoot et al. 2012).”
BackgroundMethodA longitudinal study of ICD-11 PTSD and complex PTSD in the general population of Israel
Hyland, P., Karatzias, T., Shevlin, M., Cloitre, M., & Ben-Ezra, M. (2020) · Psychiatry Research · doi:10.1016/j.psychres.2020.112871 · Cited by 37 · see citing works
Skowronski, M., Busching, R., & Krahé, B. (2021) · Sex Roles · doi:10.1007/s11199-020-01187-1 · Cited by 27 · see citing works
Kahn, D. T., Klar, Y., & Roccas, S. (2017) · Personality and Social Psychology Bulletin · doi:10.1177/0146167216684123 · Cited by 25 · see citing works
Michikyan, M., Subrahmanyam, K., Regan, P., Castillo, L. G., Ham, L., Harkness, A., & Schwartz, S. J. (2023) · Emerging Adulthood · doi:10.1177/21676968231176109 · Cited by 23 · see citing works
Edelsbrunner, P. A., Malone, S., Hofer, S. I., Küchemann, S., Kuhn, J., Schmid, R., Altmeyer, K., Brünken, R., & Lichtenberger, A. (2023) · International Journal of STEM Education · doi:10.1186/s40594-023-00435-6 · Cited by 19 · see citing works
Verschueren, M., Claes, L., Palmeroni, N., Raemen, L., Buelens, T., Moons, P., & Luyckx, K. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.667235 · Cited by 19 · see citing works
Validation and factor structure of the mindfulness-based self efficacy scale-revised
Cayoun, B., Elphinstone, B., Kasselis, N., Bilsborrow, G., & Skilbeck, C. (2022) · Mindfulness · doi:10.1007/s12671-022-01834-6 · Cited by 17 · see citing works
- Authors
- van de Schoot, R., Lugtig, P., & Hox, J.
- Affiliations
- Utrecht University (NL)
- ORCID
- Lugtig, Peter
- Venue
- European Journal of Developmental Psychology
- Publisher
- Informa UK Limited
- Published
- 2012-07
- Volume
- 9
- Issue
- 4
- Pages
- 486-492
- ISSN
- 1740-5610 (ISSN-L)
- 1740-5629
- OpenAlex
- W2166159176
- Cited by
- 2,064
- References
- 2
- Citations by year
- 2026: 138 · 2025: 170 · 2024: 177 · 2023: 233 · 2022: 227 · 2021: 234 · 2020: 189 · 2019: 175 · 2018: 136 · 2017: 128 · 2016: 95 · 2015: 78 · 2014: 50 · 2013: 21 · 2012: 9
- FWCI
- 67.05
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- European Journal of Developmental Psychology (publishedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion)
- Open Access at Essex (University of Essex) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Education › Educational Assessment and Pedagogy
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- measurement invariance, latent constructs, factor loadings, intercepts, residual variance, structural equation modeling, cross-group comparison, longitudinal assessment
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