Semiparametric Bayesian Methods for Random Effects Models

Ibrahim, Joseph G.; Kleinman, Kenneth P.

doi:10.1007/978-1-4612-1732-9_5

Cited by 11 publications

(15 citation statements)

References 16 publications

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“…For nonparametric approach, we can cite Claeskens and Hart (2009) who develop a nonparametric goodness-offit test in mixed models providing a nonparametric estimator if the normality hypothesis is rejected. Mixed models are also studied in Bayesian litterature, see Ibrahim and Kleinman (1998) who allow the prior to be nonparametric by taking a Dirichlet process.…”

Section: Introductionmentioning

confidence: 99%

Adaptive estimation of marginal random-effects densities in linear mixed-effects models

Mabon

2015

Math. Meth. Stat.

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To cite this version:Gwennaëlle Mabon. Adaptive estimation of marginal random-effects densities in linear mixed-effects models. Mathematical Methods of Statistics, Allerton Press, Springer (link), 2015, 24 (2), pp.81-102. <10.3103/S1066530715020015>. ADAPTIVE ESTIMATION OF MARGINAL RANDOM-EFFECTS DENSITIES IN LINEAR MIXED-EFFECTS MODELS G. MABONAbstract. In this paper we consider the problem of adaptive estimation of random-effects densities in linear mixed-effects model. The linear mixed-effects model is defined as Y k,j = α k + β k t j + ε k,j where Y k,j is the observed value for individual k at time t j for k = 1, . . . , N and j = 1, . . . , J. Random variables (α k , β k ) are called random effects and stand for the individual random variables of entity k. We denote their densities fα and f β and assume that they are independent of the measurement errors (ε k,j ). We introduce kernel estimators of fα and f β and present upper risk bounds. We also compute examples of rates of convergence. The focus of this work lies on the near optimal data driven choice of the smoothing parameter using a penalization strategy in the particular case of fixed interval between times t j . Risk bounds for the adaptive estimators of fα and f β are provided. Simulations illustrate the relevance of the methodology.

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Section: Introductionmentioning

confidence: 99%

Adaptive estimation of marginal random-effects densities in linear mixed-effects models

Mabon

2015

Math. Meth. Stat.

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“…The model defined in (2) is an extension of the model studied by Kleinman and Ibraham [14] and Ibrahim and Kleinman [13] where only one random effect, u i and the fixed effects have an influence on the response y i . This difference occurs because A was assumed an identity matrix by them.…”

Section: Theorymentioning

confidence: 99%

“…, k. Additionally let r represent the set of subjects with a common random effect δ r . Note that knowing the random effects is equivalent to knowing k, all of the δ's and the cluster membership r. Bush and MacEachern [3], Kleinman and Ibrahim [14] and Ibrahim and Kleinman [13] recommended one additional piece of the model as an aid to convergence for the Gibbs sampler. To speed mixing over the entire parameter space, they suggest moving around the δ's after determining how the u 's are grouped.…”

Section: Theoremmentioning

confidence: 99%

“…Other important work in this area was done by West et al [24], Escobar and West [8] and MacEachern and Müller [17]. Kleinman and Ibrahim [14] and Ibrahim and Kleinman [13] considered a Dirichlet process prior for uncorrelated random effects.…”

Section: Introductionmentioning

confidence: 99%

“…This method which is employed by transforming the numerator relationship matrix A to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and results of Kleinman and Ibrahim [14] and Ibrahim and Kleinman [13] who considered uncorrelated random effects. Also by using Gibbs sampling and data augmentation a simulation procedure is derived for estimating the precision parameter M associated with the Dirichlet process prior.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

Merwe

Pretorius

2003

Genet Sel Evol

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-In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.Bayesian methods / mixed linear model / Dirichlet process prior / correlated random effects / Gibbs sampler

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Estimating the demand for health care with panel data: a semiparametric Bayesian approach

Jochmann

Leon-Gonzalez

2004

Health Economics

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This paper is concerned with the problem of estimating the demand for health care with panel data. A random effects model is specified within a semiparametric Bayesian approach using a Dirichlet process prior. This results in a very flexible distribution for both the random effects and the count variable. In particular, the model can be seen as a mixture distribution with a random number of components, and is therefore a natural extension of prevailing latent class models. A full Bayesian analysis using Markov chain Monte Carlo simulation methods is proposed. The methodology is illustrated with an application using data from Germany.

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Semiparametric Bayesian Methods for Random Effects Models

Cited by 11 publications

References 16 publications

Adaptive estimation of marginal random-effects densities in linear mixed-effects models

Adaptive estimation of marginal random-effects densities in linear mixed-effects models

Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

Estimating the demand for health care with panel data: a semiparametric Bayesian approach

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