Assessing a Binary Measurement System with Varying Misclassification Rates Using a Latent Class Random Effects Model
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Bibliographic record
Abstract
When no gold standard measurement system is available, we can assess a binary measurement system by making repeated measurements on a random sample of parts and then using a latent class model for the analysis. However, there is widespread criticism of the model assumptions that, given the true state of the part, the repeated measurements are independent and have the same misclassification probability. We propose a latent class random effects model that relaxes these assumptions by modeling the distribution of the two misclassification rates with Beta distributions. We start by finding the likelihood, the maximum likelihood estimates (MLEs) and their approximate standard deviations with the standard assessment plan that selects parts at random from the process. However, to estimate the model parameters with reasonable precision, the standard plan requires extremely large sample sizes in the common industrial situation where the proportion of conforming parts is high and the misclassification probabilities are small. More realistic sample sizes are possible when we instead sample randomly from the population of previously failed parts and supplement the likelihood with baseline information on the overall pass rate. We show using simulation that, for feasible designs, the asymptotic standard deviation based on the expected information provides a reasonably close approximation to the simulated standard deviation. We then use these approximations to investigate how the properties of the MLEs for the unknown parameters depend on the baseline size, the number of parts in the sample, and the number of repeated measurements per part.
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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 | 0.004 | 0.002 |
| 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