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Testing measurement invariance in longitudinal data with ordered-categorical measures.

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Liu, Yu, Millsap, Roger E., West, Stephen G., Tein, Jenn-Yun, Tanaka, Rika, Grimm, Kevin J.·2017·Psychological Methods

DOI 10.1037/met0000075PMC PMC5121102

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Abstract

A goal of developmental research is to examine individual changes in constructs over time. The accuracy of the models answering such research questions hinges on the assumption of longitudinal measurement invariance: The repeatedly measured variables need to represent the same construct in the same metric over time. Measurement invariance can be studied through factor models examining the relations between the observed indicators and the latent constructs. In longitudinal research, ordered-categorical indicators such as self- or observer-report Likert scales are commonly used, and these measures often do not approximate continuous normal distributions. The present didactic article extends previous work on measurement invariance to the longitudinal case for ordered-categorical indicators. We address a number of problems that commonly arise in testing measurement invariance with longitudinal data, including model identification and interpretation, sparse data, missing data, and estimation issues. We also develop a procedure and associated R program for gauging the practical significance of the violations of invariance. We illustrate these issues with an empirical example using a subscale from the Mexican American Cultural Values scale. Finally, we provide comparisons of the current capabilities of 3 major latent variable programs (lavaan, Mplus, OpenMx) and computer scripts for addressing longitudinal measurement invariance. (PsycINFO Database Record

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Comparative fit indexes in structural models.
Bentler, P. M. (1990) · Psychological Bulletin · doi:10.1037/0033-2909.107.2.238 · Cited by 25,266
Significance tests and goodness of fit in the analysis of covariance structures.
Bentler, P. M., & Bonett, D. G. (1980) · Psychological Bulletin · doi:10.1037/0033-2909.88.3.588 · Cited by 20,015
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
Sensitivity 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
Inference and missing data
RUBIN, D. B. (1976) · Biometrika · doi:10.1093/biomet/63.3.581 · Cited by 9,925
A Reliability Coefficient for Maximum Likelihood Factor Analysis
Tucker, L. R., & Lewis, C. (1973) · Psychometrika · doi:10.1007/bf02291170 · Cited by 7,330 · cited 1×
“…measurement invariance used by standard statistical packages to calculate the CFI (and other relative fit indices like the TuckerLewis index; Tucker & Lewis, 1973) places no constraint on the mean structure or the unique factor structure, and becomes an inappropriate comparison model (cf.…”
Missing data analysis: making it work in the real world
Graham, J. W. (2009) · Annual Review of Psychology · doi:10.1146/annurev.psych.58.110405.085530 · Cited by 6,163
A scaled difference chi-square test statistic for moment structure analysis
Satorra, A., & Bentler, P. M. (2001) · Psychometrika · doi:10.1007/bf02296192 · Cited by 5,282
Principles and practice in reporting structural equation analyses.
McDonald, R. P., & Ho, M.-H. R. (2002) · Psychological Methods · doi:10.1037/1082-989x.7.1.64 · Cited by 4,734 · cited 1×
“Thus, it is important to also examine local fit indices (residuals; modification indices; cf. McDonald & Ho, 2002).”
Measurement Invariance, Factor Analysis and Factorial Invariance
Meredith, W. (1993) · Psychometrika · doi:10.1007/bf02294825 · Cited by 4,536

Show all 15 references

Research works printed but not linked: 9

Bollen KA 1989 Structural equations with latent variables New York Wiley
Browne MW Arminger G 1995 Specification and estimation of mean-and covariance-structure models Arminger G Clogg CC Sobel ME Handbook of statistical modeling for the social and behavioral sciences 185 249 New York Springer
Grimm KJ Ram N Estabrook R in press Growth modeling: An illustrative approach New York Guilford Press
Millsap RE 2011 Statistical approaches to measurement invariance New York Routledge
Mislevy RJ in press Missing responses in item response theory van der Linden WJ Hambleton RK Handbook of modern item response theory 2 2 Boca Raton, FL Chapman & Hall/CRC Press
Rosseel Y 2012 lavaan: An R package for structural equation modeling Journal of Statistical Software 48 2 1 36 http://www.jstatsoft.org/v48/i02/
Rubin DB 1987 Multiple imputation for nonresponse in surveys New York J. Wiley & Sons
Samejima F 1969 Estimation of latent ability using a response pattern of graded scores Psychometric Monograph No. 17 Richmond, VA Psychometric Society Retrieved from http://www.psychometrika.org/journal/online/MN17.pdf
Wirth RJ 2008 The effects of measurement non-invariance on parameter estimation in latent growth models Doctoral dissertation Retrieved from ProQuest dissertation and theses database. (UMI No. 3331053)

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Authors: Liu, Y., Millsap, R. E., West, S. G., Tein, J.-Y., Tanaka, R., & Grimm, K. J.
Affiliations: Arizona State University (US)
University Health Network (CA)
ORCID: Liu, Yu
Millsap, Roger E.
Tein, Jenn-Yun
Tanaka, Rika
Grimm, Kevin J.
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 2017-09
Volume: 22
Issue: 3
Pages: 486-506
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/met0000075
PMC: PMC5121102
OpenAlex: W2395889112
Cited by: 351
References: 15
Citations by year: 2026: 45 · 2025: 32 · 2024: 45 · 2023: 49 · 2022: 46 · 2021: 53 · 2020: 36 · 2019: 20 · 2018: 15 · 2017: 6
FWCI: 16.08
Type: journal article
Language: en
Open access: hybrid
doi.org
Licence: other-oa
www.apa.org/pubs/journals/resources/open-access.aspx (am)
Locations: Psychological Methods (publishedVersion, other-oa)
PubMed (publishedVersion)
Europe PMC (PubMed Central) (acceptedVersion)
PubMed Central (acceptedVersion)
Funders: National Institute of Mental Health (R01 MH68920)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
Keywords: measurement invariance, longitudinal data, factor models, system identification, data sparsity, missing data, developmental research
MeSH terms: Data Interpretation, Statistical, Factor Analysis, Statistical, Humans, Individuality, Longitudinal Studies, Models, Statistical

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Testing measurement invariance in longitudinal data with ordered-categorical measures.

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