Electronic Journal of Statistics

Flexible linear mixed models with improper priors for longitudinal and survival data

F. J. Rubio and M. F. J. Steel

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 572-598.

Dates
Received: March 2017
First available in Project Euclid: 27 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1519700495

Digital Object Identifier
doi:10.1214/18-EJS1401

Mathematical Reviews number (MathSciNet)
MR3769189

Zentralblatt MATH identifier
06864470

Subjects
Primary: 62F15: Bayesian inference 62J05: Linear regression 62N01: Censored data models

Keywords
Bayesian inference heavy tails MEAFT models posterior propriety skewness stochastic frontier models

Rights
Creative Commons Attribution 4.0 International License.

Citation

Rubio, F. J.; Steel, M. F. J. Flexible linear mixed models with improper priors for longitudinal and survival data. Electron. J. Statist. 12 (2018), no. 1, 572--598. doi:10.1214/18-EJS1401. https://projecteuclid.org/euclid.ejs/1519700495


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