Robust Two-Stage Approach Outperforms Robust Full Information Maximum Likelihood With Incomplete Nonnormal Data
Bibliographic record
Abstract
This article builds on the work of Savalei and Bentler (2009), who proposed and evaluated a statistically justified two-stage (TS) approach for fitting structural equation models with incomplete normally distributed data. The TS approach first obtains saturated maximum likelihood (ML) estimates of the population means and covariance matrix and then uses these saturated estimates in the complete data ML fitting function. Standard errors and test statistics are then adjusted to reflect uncertainty due to missing data. This work presents an extension of the TS methodology to nonnormal incomplete data (robust TS) and conducts an empirical evaluation of its performance relative to the full information maximum likelihood (FIML) approach with robust standard errors and a scaled chi-square statistic. The results indicate that although TS parameter estimates are slightly lower in efficiency, the TS approach performs better than FIML in terms of coverage and the rejection rate of the scaled chi-square across a wide variety of conditions. Its wide implementation and further study are encouraged.
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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 | 0.019 | 0.083 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".