The maximum likelihood alignment approach to testing for approximate measurement invariance: A paradigmatic cross-cultural application
Bibliographic record
Abstract
BACKGROUND: The impracticality of using the confirmatory factor analytic (CFA) approach in testing measurement invariance across many groups is now well known. A concertedeffort to addressing these encumbrances over the last decade has resulted in a new generation of alternative methodological procedures that allow for approximate, rather than exact measurement invariance across groups. The purpose of this article is twofold: (a) to describe and illustrate common difficulties encountered when tests for multigroup invariance are based on traditional CFA procedures and the number of groups is large, and (b) to walk readers through the maximum likelihood (ML) alignment approach in testing for approximate measurement invariance. METHODS: Data for this example application derive from an earlier study of family functioning across 30 cultures that include responses to the Family Values Scale for 5,482 university students drawn from 27 of these30 countries. Analyses were based on the Mplus 7.4 program. RESULTS: Whereas CFA tests for invariance revealed 108 misspecified parameters that precluded tests for latent mean differences, noninvariant results were well within the acceptable range for the alignment approach thereby substantiating the trustworthiness of the latent mean estimates and their comparison across groups. CONCLUSION: The alignment approach in testing for approximate measurement invariance provides an automated procedure that can overcome important limitations of traditional CFA procedures in large-scale comparisons.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.098 | 0.236 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.003 | 0.008 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".