Monitoring Residual Spatial Patterns using Bayesian Hierarchical Spatial Modelling for Exploring Unknown Risk Factors
Bibliographic record
Abstract
Abstract This article studies Bayesian hierarchical spatial modelling that monitors the changes of residual spatial pattern (structure) of the outcome variable for exploring unknown risk factors in small‐area analysis. Spatially structured random effects (SRE) and unstructured random effects (URE) terms added to the conventional logistic regression model take into account overdispersion and residual spatial structure, which if unaccounted for could cause incorrect identification of risk factors. Mapping and/or calculating the ratio of random effects that are spatially‐structured monitor the extent of residual spatial structure. The monitoring provides insights into identification of unknown covariates that have similar spatial structures to those of SRE. Adding such covariates to the model has the potential to diminish the residual spatial structure, until possibly all or most of the spatial structure can be explained. Risk factors identified are the added covariates that have statistically significant regression coefficients. We apply the methods to the analysis of domestic burglaries in Cambridgeshire, England. Small‐area analysis of crime where data often display apparent spatial structure would particularly benefit from the methodologies. We discuss the methodologies, their relevancy in our analysis of domestic burglaries, their limitations, and possible paths for future research.
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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 | 0.014 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".