Describing posterior distributions of variance components: Problems and the use of null distributions to aid interpretation
Bibliographic record
Abstract
Assessing the biological relevance of variance components estimated using MCMC-based mixed-effects models is not straightforward. Variance estimates are constrained to be greater than zero and their posterior distributions are often asymmetric. Different measures of central tendency for these distributions can therefore be very different, and credible intervals cannot overlap zero, making it difficult to assess the the size and statistical support for among-group variance. This is often done through visual inspection of the whole posterior distribution, and so relies on subjective decisions for interpretation. We use simulations to demonstrate the difficulties of summarising the posterior distributions of variance estimates from MCMC-based models. We compare commonly used summary statistics of posterior distributions of variance components showing that the posterior median is predominantly the least biased. We also describe different methods for generating null distributions (i.e. a distribution of effect sizes that would be obtained if there was no among-group variance) that can be used to aid in the interpretation of variance estimates. We further show how null distributions could be used to derive a p-value that provides complimentary information to the commonly presented measures of central tendency and uncertainty and also facilitates the implementation of power analyses within an MCMC framework.
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How this classification was reachedexpand
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 | 0.003 | 0.107 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".