Comparison of equilibrium and nonequilibrium estimators for the generalized production model
Bibliographic record
Abstract
Parameter estimation for the logistic (Schaefer) production model commonly uses an observation-error estimator, here termed the NM estimator, combining nonlinear-function minimization and forward projection of estimated population state. Although the NM estimator can be used to fit the generalized (PellaTomlinson) production model, an equilibrium approximation method (EA) is often used, despite calls in the literature to abandon equilibrium estimators. We examined relative merits of NM and EA estimators for the generalized model by fitting 48 000 simulated data sets describing five basic stock trajectories and widely varying population characteristics. Simulated populations followed the generalized production model exactly but were observed with random error. Both estimators were used on each data set to estimate several quantities of management interest. The estimates from NM were usually more accurate and precise than EA estimates, and overall, NM outperformed EA. This is the most comprehensive study of the question to datethe first to examine the generalized production modeland it demonstrates clearly why equilibrium estimators should be abandoned. Although valuable when introduced, they are no longer computationally necessary, they are no less demanding of data, and their performance is poor.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".