Recent Advances in Visualizing Multivariate Linear Models
Bibliographic record
Abstract
This paper reviews our work in the development of visualization methods (implemented in R) for understanding and interpreting the effects of predictors in multivariate linear models (MLMs) of the form Y = XB + U, and some of their recent extensions.We begin with a description of and examples from the Hypothesis-Error (HE) plots framework (utilizing the heplots package), wherein multivariate tests can be visualized via ellipsoids in 2D, 3D or all pairwise views for the Hypothesis and Error Sum of Squares and Products (SSP) matrices used in hypothesis tests. Such HE plots provide visual tests of significance: a term is significant by Roy’s test if and only if its H ellipsoid projects somewhere outside the E ellipsoid. These ideas extend naturally to repeated measures designs in the multivariate context. When the rank of the hypothesis matrix for a term exceeds 2, these effects can also be visualized in a reduced-rank canonical space via the candisc package, which also provides new data plots for canonical correlation problems. Finally, we discuss some recent work-in-progress: the extension of these methods to robust MLMs, and the development of generalizations of influence measures and diagnostic plots for MLMs (in the mvinfluence package).
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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 | 0.013 | 0.050 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.007 | 0.009 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.007 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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".