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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Bayesian model selection in linear mixed models for longitudinal data.

Oludare Ariyo1,2, Adrian Quintero1, Johanna Muñoz1

  • 1Leuven Biostatistics and Statistical Bioinformatics Centre (L-BioStat), KU Leuven, Leuven, Belgium.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

Marginal criteria outperform conditional criteria for selecting Bayesian linear mixed models (LMMs) in longitudinal studies. These marginal approaches, including WAIC, are crucial for accurate model selection, even with skew-normal distributions.

Keywords:
Deviance information criterionlinear mixed modelsmarginalized likelihoodpseudo-Bayes factorwidely applicable information criterion

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Linear mixed models (LMMs) are widely used for analyzing repeated measurements with Gaussian responses in longitudinal studies.
  • Model selection for fixed and random effects in LMMs is critical but lacks consensus in Bayesian frameworks.
  • Existing Bayesian criteria like DIC and pseudo-Bayes factors have limitations.

Purpose of the Study:

  • To compare the performance of Bayesian model selection criteria in LMMs, specifically focusing on marginal versus conditional criteria.
  • To evaluate these criteria in LMMs with skew-normal distributions.
  • To provide practical guidance for selecting appropriate longitudinal models.

Main Methods:

  • Comparison of deviance information criterion (DIC), pseudo-Bayes factor, and widely applicable information criterion (WAIC).
  • Evaluation of conditional criteria (given random effects) versus marginal criteria (averaged over random effects).
  • Extensive simulation study and application to Nigerian chicken growth curve data.

Main Results:

  • Marginal criteria demonstrated superior performance in selecting appropriate longitudinal models compared to conditional criteria.
  • The three marginal criteria consistently outperformed conditional approaches in the simulation study.
  • Marginal criteria successfully identified the most appropriate model for Nigerian chicken growth curves.

Conclusions:

  • Marginal Bayesian model selection criteria are recommended for longitudinal studies using LMMs.
  • The developed methods and R function facilitate the practical application of marginal criteria.
  • This research addresses a gap in Bayesian model selection for complex longitudinal data.