Bibliographic record
Abstract
The order is an important parameter in applications of finite mixture models. Yet designing a valid and easy-to-use statistical test for the order is challenging. To date, most results on hypothesis tests have focused on homogeneity, a special case where the null model has order 1. In this work, we designed an EM test for the general problem of testing the null hypothesis of order m0 versus an alternative hypothesis of order larger than m0. For any positive integer m0, the null limiting distribution of the EM test is a mixture of χ2 distributions. The weights in this mixture-limiting distribution can be conveniently computed. Compared with related results, the new result is obtained under much less strict requirements on the component distribution and the parameter space. Extensive simulation studies show that the limiting distributions closely match the finite sample distributions of the EM test. When m0 = 2, the new EM test has more accurate type I errors and matches the power of the modified likelihood ratio test. When m0 = 3, there is a clear indication that the test has good power properties. Supplementary materials for this article are available online.
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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 | 0.021 | 0.131 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".