Comparison of computationally efficient approximate methods for nonlinear and generalized linear mixed effects models
Bibliographic record
Abstract
Generalized linear mixed models (GLMMs) and nonlinear mixed effects (NLME) models are popular in the analysis of longitudinal or clustered data. Statistical inference is typically based on likelihood methods. When the number of random effects in the models is large, the observed-data likelihood function involves high-dimensional and intractable integration, as these models are nonlinear in the (unobserved) random effects. ‘Exact’ methods, such as Monte Carlo EM (MCEM) algorithms and numerical integration methods, can be computationally very intensive and may offer convergence issues. Computationally more efficient approximate methods, such as the stochastic approximation EM (SAEM) algorithm, linearization methods, or Laplace approximation methods, are therefore commonly used in practice. In this article, we conduct a comprehensive simulation study to evaluate and compare commonly used approximate methods based on three popular R packages in their current versions. Each method has its own advantages and limitations. While the performance of a method may depend on its implementation and the software version, the simulation results may still provide some useful guidelines for data analysts.
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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 | 0.022 | 0.095 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".