Parametric bootstrap and penalized quasi-likelihood inference in conditional autoregressive models
Bibliographic record
Abstract
This paper discusses a variety of conditional autoregressive (CAR) models for mapping disease rates, beyond the usual first-order intrinsic CAR model. We illustrate the utility and scope of such models for handling different types of data structures. To encourage their routine use for map production at statistical and health agencies, a simple algorithm for fitting such models is presented. This is derived from penalized quasi-likelihood (PQL) inference which uses an analogue of best-linear unbiased estimation for the regional risk ratios and restricted maximum likelihood for the variance components. We offer the practitioner here the use of the parametric bootstrap for inference. It is more reliable than standard maximum likelihood asymptotics for inference purposes since relevant hypotheses for the mapping of rates lie on the boundary of the parameter space. We illustrate the parametric bootstrap test of the practically relevant and important simplifying hypothesis that there is no spatial autocorrelation. Although the parametric bootstrap requires computational effort, it is straightforward to implement and offers a wealth of information relating to the estimators and their properties. The proposed methodology is illustrated by analysing infant mortality in the province of British Columbia in Canada.
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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 | 0.087 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".