Describing posterior distributions of variance components: Problems and the use of null distributions to aid interpretation
Bibliographic record
Abstract
Abstract Assessing the biological relevance of variance components estimated using Markov chain Monte Carlo (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 vary widely, and credible intervals cannot overlap zero, making it difficult to assess the size and statistical support for among‐group variance. Statistical support is often assessed through visual inspection of the whole posterior distribution and so relies on subjective decisions for interpretation. We use simulations to demonstrate the difficulties of summarizing the posterior distributions of variance estimates from MCMC‐based models. We then describe different methods for generating the expected null distribution (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. Through comparing commonly used summary statistics of posterior distributions of variance components, we show that the posterior median is predominantly the least biased. We further show how null distributions can be used to derive a p ‐value that provides complementary information to the commonly presented measures of central tendency and uncertainty. Finally, we show how these p ‐values facilitate the implementation of power analyses within an MCMC framework. The use of null distributions for variance components can aid study design and the interpretation of results from MCMC‐based models. We hope that this manuscript will make empiricists using mixed models think more carefully about their results, what descriptive statistics they present and what inference they can make.
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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 | 0.153 | 0.589 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.009 | 0.011 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.006 | 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".