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Flexible linear mixed models with improper priors for longitudinal and survival data
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Rubio, F. J. and Steel, Mark F. J. (2018) Flexible linear mixed models with improper priors for longitudinal and survival data. Electronic Journal of Statistics, 12 (1). pp. 572-598. doi:10.1214/18-EJS1401 ISSN 1935-7524.
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Official URL: https://doi.org/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.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Outliers (Statistics) | ||||||
Journal or Publication Title: | Electronic Journal of Statistics | ||||||
Publisher: | Institute of Mathematical Statistics | ||||||
ISSN: | 1935-7524 | ||||||
Official Date: | 27 February 2018 | ||||||
Dates: |
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Volume: | 12 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 572-598 | ||||||
DOI: | 10.1214/18-EJS1401 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 8 February 2018 | ||||||
Date of first compliant Open Access: | 18 June 2018 | ||||||
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