New Modified Estimators for the Spatial Lag Model with Randomly Missing Data in Dependent Variable: Methods and Simulation Study
Bibliographic record
Abstract
Accurately estimating the spatial lag model (SLM) in the presence of randomly missing data in the dependent variable poses a significant challenge. We introduce some modifications to the two-stage least squares with imputation (I2SLS) estimator previously proposed by Izaguirre [1] and Wang and Lee [2]. Our key contributions include (1) introducing the generalized nonlinear least squares (GNLS) estimator as an alternative imputation method to the previously used nonlinear least squares (NLS) approach in the literature, (2) incorporating additional instrument matrices (IM), and (3) implementing both partial and total imputations for all modified estimators. Through a Monte Carlo simulation (MCS) study, we evaluate the performance of these estimators across various scenarios of sample size, spatial weights matrix densities, and missingness rate. Results are compared in terms of coefficient bias and root mean squares errors (RMSE) for both the parameters and model fit. The findings indicate that all estimators demonstrate relatively strong performance in the context of estimator coefficients bias and RMSE. However, our modified estimators demonstrate slightly better performance compared to those previously documented in the literature in terms of overall RMSE. While both total and partial imputation approaches tend to produce similar results, partial imputation demonstrated superior performance in certain scenarios. Additionally, the estimators proved robust, maintaining their reliability across varying levels of spatial connectivity. However, higher missing data rates led to slightly increased bias and RMSE.
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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 | 0.017 | 0.053 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".