Normal Theory GLS Estimator for Missing Data: An Application to Item-Level Missing Data and a Comparison to Two-Stage ML
Bibliographic record
Abstract
Structural equation models (SEMs) can be estimated using a variety of methods. For complete normally distributed data, two asymptotically efficient estimation methods exist: maximum likelihood (ML) and generalized least squares (GLS). With incomplete normally distributed data, an extension of ML called "full information" ML (FIML), is often the estimation method of choice. An extension of GLS to incomplete normally distributed data has never been developed or studied. In this article we define the "full information" GLS estimator for incomplete normally distributed data (FIGLS). We also identify and study an important application of the new GLS approach. In many modeling contexts, the variables in the SEM are linear composites (e.g., sums or averages) of the raw items. For instance, SEMs often use parcels (sums of raw items) as indicators of latent factors. If data are missing at the item level, but the model is at the composite level, FIML is not possible. In this situation, FIGLS may be the only asymptotically efficient estimator available. Results of a simulation study comparing the new FIGLS estimator to the best available analytic alternative, two-stage ML, with item-level missing data are presented.
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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 | 0.057 | 0.210 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| 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".