Does strict invariance matter? Valid group mean comparisons with ordered-categorical items
Bibliographic record
Abstract
Measurement invariance (MI) of a psychometric scale is a prerequisite for valid group comparisons of the measured construct. While the invariance of loadings and intercepts (i.e., scalar invariance) supports comparisons of factor means and observed means with continuous items, a general belief is that the same holds with ordered-categorical (i.e., ordered-polytomous and dichotomous) items. However, as this paper shows, this belief is only partially true-factor mean comparison is permissible in the correctly specified scalar invariance model with ordered-polytomous items but not with dichotomous items. Furthermore, rather than scalar invariance, full strict invariance-invariance of loadings, thresholds, intercepts, and unique factor variances in all items-is needed when comparing observed means with both ordered-polytomous and dichotomous items. In a Monte Carlo simulation study, we found that unique factor noninvariance led to biased estimations and inferences (e.g., with inflated type I error rates of 19.52%) of (a) the observed mean difference for both ordered-polytomous and dichotomous items and (b) the factor mean difference for dichotomous items in the scalar invariance model. We provide a tutorial on invariance testing with ordered-categorical items as well as suggestions on mean comparisons when strict invariance is violated. In general, we recommend testing strict invariance prior to comparing observed means with ordered-categorical items and adjusting for partial invariance to compare factor means if strict invariance fails.
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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 | 0.176 | 0.547 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".