Model-Based Prediction for Small Domains Using Covariates: A Comparison of Four Methods
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Bibliographic record
Abstract
Abstract We consider methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available from the survey for all the sampled areas. Further, through an external source, there is information for all areas. The goal is to use auxiliary variables to predict the outcome of interest for all areas. We compare areal-level random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method using a horseshoe prior. Further, to measure the uncertainty of estimates obtained from random forests and the LASSO, we propose a modification of the split conformal procedure that relaxes the assumption of exchangeable data. We show that the proposed method yields intervals with the correct coverage rate and this is confirmed through a simulation study. This work is motivated by Ghanaian data available from the sixth Ghana Living Standards Survey (GLSS) and the 2010 Population and Housing Census, in the Greater Accra Metropolitan Area (GAMA) region, which comprises eight districts that are further divided into enumeration areas (EAs). We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3 percent of all the EAs (136 out of 5019) and 174 potential covariates are available in both datasets. In the application, among the four modeling methods considered, the Bayesian shrinkage performed the best in terms of bias, mean squared error (MSE), and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation with the estimated log consumption showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district has the richest areas.
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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 | 0.019 | 0.030 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.000 | 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