On the Effects of Spatial Confounding in Hierarchical Models
Why this work is in the frame
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Bibliographic record
Abstract
Summary Usually, in spatial generalised linear models, covariates that are spatially smooth are collinear with spatial random effects. This affects the bias and precision of the regression coefficients. This is known in the spatial statistics literature as spatial confounding. We discuss the problem of confounding in the case of multilevel spatial models wherein there are multiple observations within clusters. We show that even under the standard multilevel model, which allows for independent (i.e. not spatially correlated) cluster effects, the cluster‐level fixed effects might be biased depending on the structure of the ‘true’ generating mechanism of the processes. We provide simulation studies in order to investigate the effects of confounding in the estimation of fixed effects present in random intercept models under different scenarios of confounding. One remedy to spatial confounding is restricted spatial regression wherein the spatial random effects are constrained to be orthogonal to the fixed effects of the model. We propose one way to fit a restricted spatial regression model for multilevel data and illustrate it with artificial data analyses. We also briefly describe the issue of confounding in random intercept and slope models.
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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 | 0.000 | 0.003 |
| 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) | 0.002 | 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 it