Optimizing the Expected Overlap of Survey Samples via the Northwest Corner Rule
Bibliographic record
Abstract
In survey sampling there is often a need to coordinate the selection of pairs of samples drawn from two overlapping populations so as to maximize or minimize their expected overlap, subject to constraints on the marginal probabilities determined by the respective designs. For instance, maximizing the expected overlap between repeated samples can stabilize the resulting estimates of change and reduce the costs of first contacts; minimizing the expected overlap can avoid overburdening respondents with multiple surveys. We focus on the important special case in which both samples are selected by simple random sampling without replacement (SRSWOR) conducted independently within each stratum. Optimizing the expected sample overlap can be formulated as a linear programming problem known as a transportation problem (TP). We show that by appropriately grouping and ordering the possible samples in each survey, one can reduce the initial TP to a much smaller TP amenable to solution by an algorithm known as the Northwest Corner Rule (NWCR). The proposed NWCR method proceeds in two easily implemented steps: first selecting the numbers of births (new units) and deaths (deleted units) by a random selection from a hypergeometric distribution, and then selecting the births and deaths by SRSWOR. We formally prove properties of the NWCR solutions, including a minimal variance property of the minimal overlap solution. In a simulation study, the NWCR method compares favorably with a popular method based on assignment of permanent random numbers to each sampling unit.
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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 | 0.030 | 0.084 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".