Distinguishing within- from between-individual effects: How to use the within-individual centering method for quadratic patterns
Bibliographic record
Abstract
Abstract Any average pattern observed at the population level may confound two different types of processes: some processes that occur among individuals and others that occur within individuals. Separating within- from among-individual processes is critical for our understanding of ecological and evolutionary dynamics. The within-individual centering method allows distinguishing within- from among-individual processes and this method has been largely used in ecology to investigate both linear and quadratic patterns. Here we show that two alternative equations could be used for the investigation of quadratic within-individual patterns. We explain under which hypotheses each is valid. Reviewing the literature, we found that mainly one of these two equations has been used by the studies investigating quadratic patterns. Yet this equation could be inappropriate in many cases. We show that these two alternative equations make different assumptions about the shape of the within-individual pattern. The choice of using one equation instead of the other should depend upon the biological process investigated. One equation assumes that all individuals show the same quadratic pattern over the whole range of the explanatory variable whereas the other assumes that the quadratic patterns depend on the average explanatory variable of each individual. We give examples of biological processes corresponding to each equation. Using simulations, we showed that a mismatch between the assumptions made by the equation used to analyze the data and the biological process investigated led to flawed inference affecting both output of model selection and accuracy of estimates. We stress that the equation used should be chosen carefully to ensure that the assumption made about the shape of the within-individual pattern matches the biological process investigated. We hope that this manuscript will encourage the use of the within-individual centering method, promoting its correct application for non-linear relationships.
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 | 0.041 | 0.176 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".