Figure 2From “Measurement invariance before comparing English and German scores”
What each invariance result licenses
Use the invariance label to constrain the comparison sentence, not to award a generic quality score.
Figure 2What each invariance result licenses
| Result or method | What is constrained | Comparison it can support in the specified model | Stronger claim not licensed by the label alone |
|---|---|---|---|
| Configural invariance | Factor pattern and basic construct representation. | A claim that the same structural pattern is being examined across groups. | Equal item meaning, equal relations, or equal latent means. |
| Metric invariance | Factor loadings across groups. | Comparisons involving specified relations such as covariances or unstandardized regressions. | A higher or lower latent mean. |
| Scalar invariance | Loadings plus intercepts or thresholds as specified. | Latent-mean comparisons under the declared model and sample. | Permanence across samples, modes, translations, or instruments. |
| Partial invariance | Selected parameters are released while others remain equal. | The narrower comparison justified by the retained constraints and identification. | Treating every parameter as equal. |
| Approximate invariance | Small differences are allowed under an explicit tolerance or prior. | The comparison justified by that approximate model and its assumptions. | Calling the result exact or applying its tolerance universally. |
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Source: Author's comparison framework grounded in Cieciuch et al. (2014). The rows state methodological boundaries, not results for a new instrument or sample.
Source and evidence
Each line names a claim related to this exhibit, its source, and how it was checked.
- A CDAS14-C1 Measurement invariance concerns whether the same construct is measured in the same way across groups; metric and scalar invariance license different comparisonscieciuch-davidov-2014-exact-approximate-measurement-invariance
- A CDAS14-C2 Configural invariance fixes the loading pattern, metric invariance constrains loadings, and scalar invariance additionally constrains indicator interceptscieciuch-davidov-2014-exact-approximate-measurement-invariance
- A CDAS14-C4 In the cited eight-country PVQ-5X illustration, exact scalar invariance covered 10 of 19 values in the earlier analysis, while the specified approximate analysis covered all 19cieciuch-davidov-2014-exact-approximate-measurement-invariance
- A CDAS14-C5 Approximate invariance allows small parameter differences through a prior distribution and is not the same as partial invariancecieciuch-davidov-2014-exact-approximate-measurement-invariance
Grades: A, verified against the printed page of the primary source · B, primary source, text layer only · C, authoritative secondary · D, reported.
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Measurement invariance before comparing English and German scores
A translated scale is not automatically comparable: configural, metric, and scalar invariance license different cross-language claims.
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