A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions

Author(s)

Lachos, Victor H. ^[1] ; Cabral, Celso R. B. ^[2] ; Abanto-Valle, Carlos A. ^[3]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Dept Stat, BR-13083859 Sao Paulo - Brazil

^[2] Univ Fed Amazonas, Dept Stat, BR-69080005 Manaus, Amazonas - Brazil

^[3] Univ Fed Rio de Janeiro, Dept Stat, BR-21945970 Rio De Janeiro, RJ - Brazil

• Document type: Journal article
• Source: Journal of Applied Statistics; v. 39, n. 3, p. 531-549, 2012.
• Web of Science Citations: 4

Abstract

In this paper, we utilize normal/independent (NI) distributions as a tool for robust modeling of linear mixed models (LMM) under a Bayesian paradigm. The purpose is to develop a non-iterative sampling method to obtain i.i.d. samples approximately from the observed posterior distribution by combining the inverse Bayes formulae, sampling/importance resampling and posterior mode estimates from the expectation maximization algorithm to LMMs with NI distributions, as suggested by Tan et al. {[}33]. The proposed algorithm provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. In order to examine the robust aspects of the NI class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on model selection criteria are given. The new methodologies are exemplified through a real data set, illustrating the usefulness of the proposed methodology. (AU)

• FAPESP's process: 08/11455-0 - Robust models with scale mixtures of Skew-normal distributions
• Grantee: Víctor Hugo Lachos Dávila
• Support Opportunities: Regular Research Grants