On the uncanny relationship between nonnormality and moderated multiple regression.
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Moderated multiple regression is one of the most established, popular methods to model nonlinear associations in social sciences. A mostly unacknowledged fact is that a particular type of nonnormality can make the coefficient capturing this association nonzero. To further understand this connection, a theoretical investigation was conducted. A generalization of Isserlis' theorem from multivariate normal densities to all elliptical densities is presented. Through this generalization, it was found that the family of elliptical densities (which includes the multivariate normal) cannot generate a product-interaction term. Moreover, asymmetry in lower and/or higher dimensions can induce a product-interaction term. Special case studies are presented where the variables are unidimensional symmetric, but jointly nonsymmetric, resulting in a moderated multiple regression model. A call is made for researchers to think carefully and decide when they have a true interaction term, theorized a priori, and when nonnormality is mimicking an interaction effect. (PsycInfo Database Record (c) 2026 APA, all rights reserved).
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.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.035 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it