Comparing the Accuracy of Three Predictive Information Criteria for Bayesian Linear Multilevel Model Selection
Bibliographic record
Abstract
Bayesian multilevel modeling techniques have become increasingly popular. As researchers leverage these techniques, information criteria—fit indices which provide information about a model’s fit to the data—play an important role in disambiguating between competing models. The deviance information criteria (DIC) has been historically popular and is computationally easy, yet newer indices such as Watanabe-Akaike information criterion (WAIC) and an approximation to the leave-one-out cross-validation information criterion (LOO-CV) have been recently introduced. However, researchers may be unsure about which criteria to use, as to our knowledge, a systematic evaluation of these Bayesian criteria in a multilevel context has not yet been undertaken. Complicating this matter, computation of these indices using the so-called marginal likelihood is sometimes recommended, yet use of the conditional likelihood is easier and more readily found in some popular software. In addition, researchers frequently select the model with the lowest value of the information criteria, discounting the presence of uncertainty in calculating the criteria. Across two extensive simulation studies meant to mimic experimental and observational studies, we investigate the model selection accuracy of conditional and marginal versions of DIC, WAIC, and LOO-CV; we also compare a lowest wins strategy versus one that considers model selection uncertainty. In general, indices based on the marginal likelihood had a slight advantage and performed similarly to each other, whereas under the conditional likelihood WAIC and LOO-CV outperformed DIC. In addition, we argue that a selection strategy that simply chooses the model with the lowest information criteria may result in overfitting.
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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 | 0.114 | 0.338 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.010 | 0.006 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.006 | 0.006 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.004 | 0.006 |
| 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".