CONFIDENCE INTERVALS FOR THE OPTIMUM IN THE GAUSSIAN RESPONSE FUNCTION
Bibliographic record
Abstract
The optimum of a species on a gradient is an important parameter for ecological interpretation and bioindication. The location of the optimum is easily estimated in the popular Gaussian response model, but it is more difficult to assess the precision of the estimated optima. Methods based on the profile likelihood or quasilikelihood function are presented to find confidence intervals for the optimum parameter of the Gaussian response function using generalized linear models. The following four cases are considered: optimum on one gradient; optimum on one gradient when there are additional stratifying variables; optimum on an interesting gradient at a certain level of a stratifying variable when the optimum is dependent on the latter; and simultaneous confidence region for the joint overall optimum on two gradients. The methods are illustrated with two species of testate amoebae (Protozoa: Rhizopoda) in Finnish mires. The first two cases were also analyzed using Fieller's theorem, although it produced generally wider limits.
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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 | 0.049 | 0.253 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".