A combined moment equation approach for spatial autoregressive models
Bibliographic record
Abstract
Abstract Existing methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two‐stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".