Testing measurement invariance in longitudinal data with ordered-categorical measures.
Open accessAbstract
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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Longitudinal measurement invariance was tested by comparing a series of nested factor models, adding specific restrictions.
“To do so, we tested for longitudinal measurement invariance by comparing a series of nested factor models, adding specific restrictions to the models65,66.”
From Adolescent leisure reading and its longitudinal association with prosocial behavior and social adjustment (2023) · cites this paper as [66]
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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)
- Venue
- Psychological Methods
- Published
- 2017-09
- Volume
- 22
- Issue
- 3
- Pages
- 486-506
- ISSN
- 1082-989X (ISSN-L)
- 1939-1463
- 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 · 2016: 3
- FWCI
- 16.08
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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