Comparisons of the Satterthwaite Approaches for Fixed Effects in Linear Mixed Models
Bibliographic record
Abstract
Four approximate F- tests derived by Fai and Cornelious in 1996 to make inference for fixed effects in mixed linear models of rank greater than one. Two of these approaches derived by introducing a Wald-type statistic distributed approximately as an F distribution, and the denominator degrees of freedom computed by matching the approximated one moment of the Wald-type statistic with the exact one moment of the F distribution. The other two approaches were derived by introducing a scaled Wald-type statistic to be distributed approximately as an F distribution, and the denominator degrees of freedom and the scale factor computed by matching the two moments of the statistic with the moments of the F distribution. This paper proposes two more approximate F-tests analogous to the four approaches where an adjusted estimator of the variance of the estimate of fixed effects used. In addition, the paper evaluates and compares the performance of the six approaches analytically, and some useful results are presented. Also, a simulation study for block designs was run to assess and compare the performance of the approaches based on their observed test levels. The simulation study shows that the approaches usually perform reasonably based on their test levels, and in some cases some approaches found to more adequately than other approaches.
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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 | 0.152 | 0.479 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.007 |
| Bibliometrics | 0.007 | 0.006 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.004 | 0.006 |
| 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".