A Comparison of Scaled Difference Tests for Forming Confidence Intervals in SEM
Bibliographic record
Abstract
Likelihood-based confidence intervals often perform better than Wald-based intervals in structural equation modeling. One challenge involves their robustness to nonnormality. While prior research has implemented a “robust” variant based on one scaled test, other scaled difference tests are available. In addition, lavaan-based software implementations are challenging and several solutions, including the semlbci package, have not been compared. We report two simulations evaluating three scaled difference tests and two software implementations; we also include bootstrapping, Bayesian estimation, and Wald-based intervals based on a sandwich covariance matrix with observed information (Huber-White or “MLR”). We vary nonnormality and examined a behavioral genetics model and a cross-lagged panel model with an indirect effect. The originally used scaled test outperformed other scaled tests, was comparable to bootstrapping, and slightly outperformed MLR under certain nonnormality conditions with the behavioral genetics model. We document challenges in estimation of these intervals with lavaan.
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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 | 0.095 | 0.529 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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".