An analysis and comparison of estimation methods for self-referencing equations
Bibliographic record
Abstract
Self-referencing equations (SREs) play an important role in modeling stand and individual-tree growth and yield. Over the decades, forest modelers have applied ordinary least-squares (OLS) or generalized least-squares to fit SREs (namely, the SRE method). In this article, we discuss the statistical properties of the SRE method via theoretical and empirical analyses. The SRE method has its disadvantages: (i) the parameter estimates are not the OLS estimates; (ii) the standard errors of the parameters are underestimated; (iii) the model mean squared error is overestimated; and (iv) the model random errors are always correlated and have heterogeneous variances. Thus, statistical inferences based on these model statistics may not be valid. In addition, there is no simple way to overcome these problems, because they arise from the data structures used for model fitting. This study demonstrates that the disadvantages of the SRE method can be circumvented by fitting the corresponding base model, rather than the transformed model, using two alternative methods: dummy variable regression (DVR method) and mixed effect models (MIX method). The DVR and MIX methods can efficiently account for serial autocorrelation and variance heterogeneity and, thus, produce valid model statistics for hypothesis testing and confidence intervals.
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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 | 0.075 | 0.251 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 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".