Implications of confounding from unmodeled interactions between explanatory variables when using latent variable regression models to make inferences
Bibliographic record
Abstract
With linear dependency between the explanatory variables, partial least squares (PLS) regression is commonly used for regression analysis. If the response variable correlates to a high degree with the explanatory variables, a model with excellent predictive ability can usually be obtained. Ranking of variable importance is commonly used to interpret the model and sometimes this interpretation guides further experimentation. For instance, when analyzing natural product extracts for bioactivity, an underlying assumption is that the highest ranked compounds represent the best candidates for isolation and further testing. A problem with this approach is that in most cases the number of compounds is larger than the number of samples (and usually much larger) and that the concentrations of the compounds correlate. Furthermore, compounds may interact as synergists or as antagonists. If the modelling process does not account for this possibility, the interpretation can be thoroughly wrong since unmodelled variables that strongly influence the response will give rise to confounding of a first order PLS model and send the experimenter on a wrong track. We show the consequences of this by a practical example from natural product research. Furthermore, we show that by including the possibility of interactions between explanatory variables, visualization using a selectivity ratio plot may provide model interpretation that can be used to make inferences.
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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 | 0.151 | 0.360 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.003 | 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".