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2018 Flexible linear mixed models with improper priors for longitudinal and survival data
F. J. Rubio, M. F. J. Steel
Electron. J. Statist. 12(1): 572-598 (2018). DOI: 10.1214/18-EJS1401

Abstract

We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture tails heavier than those of the normal distribution. This generalisation is useful to produce models that are robust to the presence of outliers. The case of asymmetric residual errors is also studied. We present general results for the propriety of the posterior that also cover cases with censored observations, allowing for the use of these models in the contexts of popular longitudinal and survival analyses. We consider the use of copulas with flexible marginals for modelling the dependence between the random effects, but our results cover the use of any random effects distribution. Thus, our paper provides a formal justification for Bayesian inference in a very wide class of models (covering virtually all of the literature) under attractive prior structures that limit the amount of required user elicitation.

Citation

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F. J. Rubio. M. F. J. Steel. "Flexible linear mixed models with improper priors for longitudinal and survival data." Electron. J. Statist. 12 (1) 572 - 598, 2018. https://doi.org/10.1214/18-EJS1401

Information

Received: 1 March 2017; Published: 2018
First available in Project Euclid: 27 February 2018

zbMATH: 06864470
MathSciNet: MR3769189
Digital Object Identifier: 10.1214/18-EJS1401

Subjects:
Primary: 62F15, 62J05, 62N01

JOURNAL ARTICLE
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Vol.12 • No. 1 • 2018
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