Frequentist Conditional Variance for Nonlinear Mixed-Effects Models
Bibliographic record
Abstract
Abstract Nonlinear mixed-effects models are commonly used in fisheries and ecological studies to account for complex relationships and dependencies in data. These models involve both fixed parameters to estimate and random-effects (REs) to predict. This paper addresses the inferential setting involving repeated sampling of the data but conditional on the unknown REs. This setting is more appropriate when the focus is on statistical inferences based on the specific values of REs that generated the data. Assuming the Laplace approximation is appropriate to derive the marginal likelihood and following a frequentist framework, this work derives RE-conditional bias approximations of maximum likelihood parameter estimators and empirical Bayes RE predictors, as well as the conditional covariance and mean squared error (MSE) among parameter estimators and RE predictors. It is shown that the RE-conditional MSE can be approximated with the unconditional MSE. Simulation studies demonstrate that the variance and MSE approximations are reasonably accurate for relevant sample sizes. Considering the finite-sample RE-conditional biases in the parameter estimates and RE predictions, the MSE is more appropriate for constructing confidence intervals (CIs), and the CI coverage of REs should be interpreted as the average coverage over a range of REs or over repeated generation of REs.
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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 | 0.024 | 0.089 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".