Measurement invariance

Measurement invariance is the condition in which a measure represents the same construct in comparable ways across groups, settings, or time points.

Configural invariance: The same pattern of measured indicators and latent factors holds across groups or occasions. It is the baseline test: groups must share the measure’s basic factor structure.
Multiple-group confirmatory factor analysis: A confirmatory factor analysis that estimates and compares measurement models across distinct groups. It is a standard framework for testing invariance across populations.
Measurement equivalence: The broader idea that a measure functions comparably across populations, settings, or occasions. It is often used alongside invariance, though terminology and criteria vary by field.
Partial measurement invariance: A condition in which some, but not all, measurement parameters are equal across groups or occasions. It can permit limited comparisons when a small number of parameters are noninvariant.
Metric invariance: A condition in which corresponding factor loadings are equal across groups or occasions. Equal loadings support comparisons of associations involving the latent construct.
Longitudinal measurement invariance: Measurement invariance assessed across repeated observations of the same individuals over time. It distinguishes genuine change from shifts in how a measure functions over time.
Observed-score comparison: A comparison of recorded scale scores without establishing that the measure functions equivalently across groups. Observed differences can reflect item or scale bias rather than differences in the construct.
Alignment optimization: A method for estimating approximate measurement invariance across many groups by minimizing parameter noninvariance. It offers an alternative when exact invariance tests across numerous populations are impractical.
Scalar invariance: A condition in which corresponding item intercepts, as well as factor loadings, are equal across groups or occasions. Equal intercepts make latent mean comparisons interpretable.
Cross-cultural research: Research comparing social, psychological, or behavioral phenomena across cultural settings. Cross-cultural comparisons need evidence that translated or adapted measures retain comparable meaning.

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