Robust Small-Sample Inference for Fixed Effects in General Gaussian Linear Models
Bibliographic record
Abstract
Although asymptotically, the empirical covariance estimator is consistent and robust with respect to the selection of the working correlation matrix, when the sample size is small, its bias may not be negligible. This article proposes a small sample correction for the empirical covariance estimator in general Gaussian linear models. Inference for the fixed effects based on the corrected covariance matrix is also derived. A two-way analysis of variance (ANOVA) model with repeated measures, which evaluates the effectiveness of a CB1 receptor antagonist, and a four-period crossover design, which assesses the treatment effect in subjects with intermittent claudication, serve as examples to illustrate the proposed and other investigated methods. Simulation studies show that the proposed method generally performs better than other bias-correction methods, including Mancl and DeRouen (2001 Mancl , L. A. , DeRouen , T. A. ( 2001 ). A covariance estimator for GEE with improved small-sample properties . Biometrics 57 : 126 – 134 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), Kauermann and Carroll (2001 Kauermann , G. , Carroll , R. J. ( 2001 ). A note on the efficiency of sandwich covariance matrix estimation . Journal of the American Statistical Association 96 : 1387 – 1396 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and Fay and Graubard (2001 Fay , M. P. , Graubard , B. I. ( 2001 ). Small-sample adjustments for Wald-type tests using sandwich estimators . Biometrics 57 : 1198 – 1206 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), in the investigated balanced designs.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.108 | 0.382 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.005 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.006 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 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".