## Variable Selection in Nonparametric Random Effects Models

Citations: | 2 - 2 self |

### BibTeX

@MISC{Cai_variableselection,

author = {Bo Cai and David B. Dunson and Biostatistics Branch and Md A},

title = {Variable Selection in Nonparametric Random Effects Models},

year = {}

}

### OpenURL

### Abstract

In analyzing longitudinal or clustered data with a mixed effects model (Laird and Ware, 1982), one may be concerned about violations of normality. Such violations can potentially impact subset selection for the fixed and random effects components of the model, inferences on the heterogeneity structure, and the accuracy of predictions. This article focuses on Bayesian methods for subset selection in nonparametric random effects models in which one is uncertain about the predictors to be included and the distribution of their random effects. We characterize the unknown distribution of the individual-specific regression coefficients using a weighted sum of Dirichlet process (DP)-distributed latent variables. By using carefully-chosen mixture priors for coefficients in the base distributions of the component DPs, we allow fixed and random effects to be effectively dropped out of the model. A stochastic search Gibbs sampler is developed for posterior computation, and the methods are illustrated using simulated data and real data from a multi-laboratory bioassay study.

### Citations

714 |
A bayesian analysis of some nonparametric problems
- Ferguson
- 1973
(Show Context)
Citation Context ... (2001), Chen, Zhang and Davidian (2002), Lai and Shih (2003), and Ghidey, Lesaffre and Eilers (2004). In addition, there is a rich literature on Bayesian methods using Dirichlet process (DP) priors (=-=Ferguson, 1973-=-), DP mixtures (DPM) (Antoniak, 1974), and other specifications to allow unknown random effects distributions (Bush and MacEachern, 1996; Kleinman and Ibrahim, 1998; Ishwaran and Takahara, 2002; Lopes... |

418 |
Mixtures of dirichlet processes with applications to bayesian nonparametric problems
- Antoniak
- 1974
(Show Context)
Citation Context ...002), Lai and Shih (2003), and Ghidey, Lesaffre and Eilers (2004). In addition, there is a rich literature on Bayesian methods using Dirichlet process (DP) priors (Ferguson, 1973), DP mixtures (DPM) (=-=Antoniak, 1974-=-), and other specifications to allow unknown random effects distributions (Bush and MacEachern, 1996; Kleinman and Ibrahim, 1998; Ishwaran and Takahara, 2002; Lopes, Müller and Rosner, 2003; Müller et... |

400 | Bayesian density estimation and inference using mixtures
- Escobar, West
- 1995
(Show Context)
Citation Context ...abilities for the possible submodels, estimated posterior means, and 95% credible intervals for each of the parameters. To obtain proper samples of αh, we ran 20 sub-iterations within each iteration (=-=Escobar and West, 1995-=-). To compare the results of our nonparametric mixed effect analysis (NME) with other approaches, we also fit a frequentist linear mixed effects model (LME) and applied Chen and Dunson’s method (CDM) ... |

316 |
Random-effects models for longitudinal data
- Laird, Ware
- 1982
(Show Context)
Citation Context ...cs Branch, MD A3-03 National Institute of Environmental Health Sciences P.O. Box 12233 Research Triangle Park, NC 27709, U.S.A. In analyzing longitudinal or clustered data with a mixed effects model (=-=Laird and Ware, 1982-=-), one may be concerned about violations of normality. Such violations can potentially impact subset selection for the fixed and random effects components of the model, inferences on the heterogeneity... |

314 | A Constructive Definition of Dirichlet Priors - Sethuraman - 1994 |

276 | Evaluating the accuracy of sampling-based approaches to calculating posterior moments - Geweke - 1992 |

266 |
Ferguson distributions via polya urn schemes
- Blackwell, MacQueen
- 1973
(Show Context)
Citation Context ...on the covariance structure between random effects in the model, this prior can be adapted to include mass at zero One of the most useful properties of the DP prior is the Pólya urn characterization (=-=Blackwell and MacQueen, 1973-=-), which was exploited by Escobar (1994), MacEachern (1994), and West et al. (1994). Let Sh = (S1h, . . . , Snh) ′ denote a configuration of β ∗ h = (β1h, . . . , βnh) ′ into kh ≤ n distinct values θh... |

138 | Bayesian measures of model complexity and fit
- Spiegelhalter, Best, et al.
- 2002
(Show Context)
Citation Context ...sents the posterior probabilities of all submodels selected by our nonparametric mixed effect method and Chen and Dunson’s method. We also show the corresponding deviance information criterion (DIC) (=-=Spiegelhalter et al, 2002-=-), obtained by running separate linear mixed effects model analyses for each model in the list. Although each method chooses the true model as the best model, our NME approach assigns higher posterior... |

126 | Approaches for Bayesian variable selection
- George, McCulloch
- 1997
(Show Context)
Citation Context ...roblems, the number of possible models is typically very large, and it is necessary to develop an automated search procedure that does not require fitting of all the models in the list (Geweke, 1996; =-=George and McCulloch, 1997-=-). For a review of Bayesian approaches to this problem in parametric models, refer to Clyde and George (2004). Chen and Dunson (2003) proposed a Bayesian approach for random effects selection in the n... |

103 |
Estimating Normal means with a Dirichlet process prior
- Escobar
- 1994
(Show Context)
Citation Context ...roposed MCMC algorithm proceeds as follows: 1. Update β∗ ih , for i = 1, . . . , n and h = 1, . . . , p, from the full conditional posterior distribution of β ∗ ih derived using the Pólya urn scheme (=-=Escobar, 1994-=-; MacEachern, 1994; West et al., 1994) given the data and current values of θ (i) h , β, Γ, S(i) h and σ. 2. Update αh, for h = 1, . . . , p, from the full conditional posterior distribution by updati... |

101 |
Estimating normal means with a conjugate style dirichlet process prior
- MacEachern
- 1994
(Show Context)
Citation Context ...gorithm proceeds as follows: 1. Update β∗ ih , for i = 1, . . . , n and h = 1, . . . , p, from the full conditional posterior distribution of β ∗ ih derived using the Pólya urn scheme (Escobar, 1994; =-=MacEachern, 1994-=-; West et al., 1994) given the data and current values of θ (i) h , β, Γ, S(i) h and σ. 2. Update αh, for h = 1, . . . , p, from the full conditional posterior distribution by updating latent paramete... |

98 |
A semiparametric bayesian model for randomised block designs
- Bush, MacEachern
- 1996
(Show Context)
Citation Context ...a rich literature on Bayesian methods using Dirichlet process (DP) priors (Ferguson, 1973), DP mixtures (DPM) (Antoniak, 1974), and other specifications to allow unknown random effects distributions (=-=Bush and MacEachern, 1996-=-; Kleinman and Ibrahim, 1998; Ishwaran and Takahara, 2002; Lopes, Müller and Rosner, 2003; Müller et al., 2005; among others). All of these methods do not accommodate uncertainty in the predictors to ... |

91 | Hierarchical priors and mixture models, with application in regression and density estimation. In: Aspects of Uncertainty: A tribute to
- West, Müller, et al.
- 1994
(Show Context)
Citation Context ...s follows: 1. Update β∗ ih , for i = 1, . . . , n and h = 1, . . . , p, from the full conditional posterior distribution of β ∗ ih derived using the Pólya urn scheme (Escobar, 1994; MacEachern, 1994; =-=West et al., 1994-=-) given the data and current values of θ (i) h , β, Γ, S(i) h and σ. 2. Update αh, for h = 1, . . . , p, from the full conditional posterior distribution by updating latent parameter φh based on the m... |

64 | Variable selection and model comparison in regression
- Geweke
- 1996
(Show Context)
Citation Context ...et selection problems, the number of possible models is typically very large, and it is necessary to develop an automated search procedure that does not require fitting of all the models in the list (=-=Geweke, 1996-=-; George and McCulloch, 1997). For a review of Bayesian approaches to this problem in parametric models, refer to Clyde and George (2004). Chen and Dunson (2003) proposed a Bayesian approach for rando... |

24 | Parameterizations for Normal Linear Mixed Models - Gelfand, Sahu, et al. - 1995 |

24 |
The OECD program to validate the rat uterotrophic bioassay to screen compounds for in vivo estrogenic responses: phase 1,” Environmental Health Perspectives
- Kanno, Onyon, et al.
- 2001
(Show Context)
Citation Context ...te our approach through analysis of data from an international validation study of the rat uterotrophic bioassay, a new animal model designed to detect in vivo estrogenic responses to test chemicals (=-=Kanno et al., 2001-=-). The data were collected from 19 participating laboratories in 8 nations and consisted of 2681 female rats. One or more out of four protocols were chosen by each laboratory. Two of the protocols use... |

24 |
A semi-parametric Bayesian approach to the random effects model
- K, Ibrahim
- 1998
(Show Context)
Citation Context ...an methods using Dirichlet process (DP) priors (Ferguson, 1973), DP mixtures (DPM) (Antoniak, 1974), and other specifications to allow unknown random effects distributions (Bush and MacEachern, 1996; =-=Kleinman and Ibrahim, 1998-=-; Ishwaran and Takahara, 2002; Lopes, Müller and Rosner, 2003; Müller et al., 2005; among others). All of these methods do not accommodate uncertainty in the predictors to be included in the fixed and... |

22 | Marginal likelihood and Bayes factors for Dirichlet process mixture models - Basu, Chib - 2003 |

18 | Random effects selection in linear mixed models - Chen, Dunson - 2003 |

18 | Nonparametric empirical bayes for the dirichlet process mixture model - McAuliffe, Blei, et al. - 2006 |

16 | Bayesian tests and model diagnostics in conditionally independent hierarchical models - Albert, Chib - 1997 |

14 | How many iterations in the Gibbs sampler,” Bayesian statistics - Raftery, Lewis - 1992 |

14 |
The use of score tests for inference on variance components
- Verbeke, Molenberghs
(Show Context)
Citation Context ...ponents are zero. Lin’s approach does not require specification of a parametric form for the random effects density. Later authors have considered alternative score tests (Hall and Praestgaard, 2001; =-=Verbeke and Molenberghs, 2003-=-; Zhu and Fung, 2004) and generalized likelihood ratio tests (Craniniceaunu and Ruppert, 2004). These methods are not useful for the general subset selection problem. Bayesian methods for the model co... |

13 | Independent and identically distributed monte carlo algorithms for semiparametric linear mixed models
- Ishwaran, Takahara
- 2002
(Show Context)
Citation Context ...rocess (DP) priors (Ferguson, 1973), DP mixtures (DPM) (Antoniak, 1974), and other specifications to allow unknown random effects distributions (Bush and MacEachern, 1996; Kleinman and Ibrahim, 1998; =-=Ishwaran and Takahara, 2002-=-; Lopes, Müller and Rosner, 2003; Müller et al., 2005; among others). All of these methods do not accommodate uncertainty in the predictors to be included in the fixed and random effects components of... |

13 | Variance component testing in generalised linear models with random effects - Lin - 1997 |

9 | Linear mixed models with flexible distributions of random effects for longitudinal data - Zhang, Davidian - 2001 |

8 | Bayesian covariance selection in generalized linear mixed models
- Cai, Dunson
- 2006
(Show Context)
Citation Context ...hart prior is not sufficiently flexible. For this reason, Chen and Dunson (2003) proposed a reparameterization of model (1) based on a decomposition of Σ that facilitated variable selection (see also =-=Cai and Dunson, 2005-=-). The Chen and Dunson (2003) approach relies on the incorporation of standard normal latent variables underlying the random effects. Therefore, the approach does not generalize naturally to the nonpa... |

8 | Bayes factors and approximations for variance component models - Pauler, Wakefield, et al. - 1999 |

7 |
Order-restricted score tests for homogeneity in generalized linear and nonlinear mixed models
- Hall, Praestgaard
- 2001
(Show Context)
Citation Context ...thesis that all variance components are zero. Lin’s approach does not require specification of a parametric form for the random effects density. Later authors have considered alternative score tests (=-=Hall and Praestgaard, 2001-=-; Verbeke and Molenberghs, 2003; Zhu and Fung, 2004) and generalized likelihood ratio tests (Craniniceaunu and Ruppert, 2004). These methods are not useful for the general subset selection problem. Ba... |

7 | Bayesian meta-analysis for longitudinal data models using multivariate mixture priors - Lopes, Muller, et al. - 2003 |

6 | Examples in which misspecification of a random effects distribution reduces efficiency and possible remedies - AGRESTI, OHMAN, et al. - 2004 |

6 | A Monte Carlo EM Algorithm for Generalized Linear Mixed Models with Flexible Random Effects Distribution - Chen, Zhang, et al. - 2002 |

6 | Smooth random effects distribution in a linear mixed modeling - Ghidey, Lesaffre, et al. - 2004 |

6 | Nonparametric estimation in nonlinear mixed effects models, Biometrika 90 - Lai, Shih - 2003 |

5 | A nonparametric Bayesian model for inference in related longitudinal studies - Muller, Rosner, et al. |

5 | Bayes Factors for Variance Component Testing in Generalized Linear Mixed Models,” Doctoral dissertation - Sinharay - 2001 |

2 | Restricted likelihood ratio tests in nonparametric longitudinal models - Crainiceaunu, Ruppert - 2004 |