Fit indices are insensitive to multiple minor violations of perfect simple structure in confirmatory factor analysis.
Bibliographic record
Abstract
Classic confirmatory factor analysis (CFA) models are theoretically superior to exploratory factor analysis (EFA) models because they specify that each indicator only measures one factor. In contrast, in EFA, all loadings are permitted to be nonzero. In this article, we show that when fit to EFA structures and other models with many cross-loadings, classic CFA models often produce excellent fit. A key requirement for breaking this pattern is to have highly variable ratios of main loadings to corresponding cross-loadings in the true data-generating structure-and strongest misfit results when cross-loadings are of mixed sign. We show mathematically that EFA structures that are rotatable to a CFA representation are those where the main loadings and the cross-loadings are proportional for each group of indicators. With the help of a ShinyApp, we show that unless these proportionality constraints are violated severely in the true data structure, CFA models will fit well to most true models containing many cross-loadings by commonly accepted fit index cutoffs. We also show that fit indices are nonmonotone functions of the number of positive cross-loadings, and the relationship becomes monotone only when cross-loadings are of mixed sign. Overall, our findings indicate that good fit of a CFA model rules out that the true model is an EFA model with highly variable ratios of main and cross-loadings, but does not rule out most other plausible EFA structures. We discuss the implications of these findings. (PsycInfo Database Record (c) 2025 APA, all rights reserved).
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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 | 0.254 | 0.723 |
| Meta-epidemiology (narrow) | 0.004 | 0.005 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.011 | 0.017 |
| Science and technology studies | 0.004 | 0.011 |
| Scholarly communication | 0.009 | 0.015 |
| Open science | 0.006 | 0.008 |
| Research integrity | 0.005 | 0.011 |
| Insufficient payload (model declined to judge) | 0.011 | 0.008 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".