{
  "abstract": "Bayesian multilevel models are increasingly used in psychological, educational, and behavioral research, yet applied guidance on specifying priors for scalar variance components remains limited. This tutorial provides a practical workflow for identifying target variance components, selecting benchmark values, calibrating priors on variance and standard-deviation scales, translating them into software-compatible prior specifications, evaluating their implications through prior predictive checks, posterior comparison, sensitivity analysis, and transparent reporting. We review several commonly used prior families, including gamma, inverse-gamma, half-t, and half-Cauchy distributions, and clarify how their parameterizations relate across variance, precision (the reciprocal of variance), and standard-deviation formulations. The tutorial focuses on helping researchers align prior choice with substantive knowledge, model parameterization, software constraints, and sensitivity goals. As a worked example, we use a two-level analysis of TIMSS 2019 data to show how benchmark information from a non-overlapping reference sample can be calibrated into alternative variance-prior specifications and then evaluated in a smaller worked example sample. The empirical illustration is used as a pedagogical example to demonstrate the workflow and its associated checking procedures. We emphasize practical safeguards, including prior-density inspection, prior predictive checking, posterior comparison, convergence assessment, sensitivity analysis, and transparent reporting of prior assumptions. The tutorial concludes by summarizing practical, literature-grounded considerations for documenting prior rationale, implementation decisions, and robustness checks in Bayesian multilevel applications.",
  "abstract_shown": true,
  "affiliations": [
    "School of Social Work, University of Georgia, Athens, GA, 30602, USA. liuuil@uga.edu."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Liu Liu",
      "orcid": "0000-0001-6900-9829"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s76tfyzg89s4.bib",
  "cited_by": 0,
  "doi": "10.3758/s13428-026-03201-y",
  "fulltext_url": "https://europepmc.org/articles/PMC13680335",
  "id": "1s76tfyzg89s4",
  "issns": [
    "1554-351X",
    "1554-3528"
  ],
  "landing_url": "https://europepmc.org/article/MED/42897411",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2613|Statistical Methods and Bayesian Inference"
    ]
  ],
  "openalex": "W7221578839",
  "pdf_url": "https://europepmc.org/articles/PMC13680335?pdf=render",
  "pmcid": "PMC13680335",
  "pmid": "42897411",
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s76tfyzg89s4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:32Z",
      "native_id": "MED:42897411",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42897411"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Methods and Bayesian Inference",
      "subfield": "statistics"
    }
  ],
  "title": "A tutorial on selecting, translating, and reporting variance priors in Bayesian multilevel models.",
  "title_text": "A tutorial on selecting, translating, and reporting variance priors in Bayesian multilevel models.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:19:32Z",
  "url": "https://research.draconitic.com/paper/1s76tfyzg89s4",
  "venue": "Behavior research methods",
  "versions": []
}