Additive mixed models with Dirichlet process mixture and P-spline priors
نویسندگان
چکیده
Longitudinal data often require a combination of flexible trends and individual-specific random effects. In this paper, we propose a fully Bayesian approach based on Markov chain Monte Carlo simulation techniques that allows for the semiparametric specification of both the trend function and the random effects distribution. Bayesian penalized splines are considered for the former, while a Dirichlet process mixture (DPM) specification allows for an adaptive amount of deviations from normality for the latter. We investigate the advantages of DPM prior structures for random effects in terms of a simulation study and present a challenging application that requires semiparametric mixed modeling.
منابع مشابه
Package ‘ DPpackage ’ March 15 , 2010
Description This package contains functions to perform inference via simulation from the posterior distributions for Bayesian nonparametric and semiparametric models. Although the name of the package was motivated by the Dirichlet Process prior, the package considers and will consider other priors on functional spaces. So far, DPpackage includes models considering Dirichlet Processes, Dependent...
متن کاملBayesian hierarchical linear mixed models for additive smoothing splines
Bayesian hierarchical models have been used for smoothing splines, thin-plate splines, and L-splines. In analyzing high dimensional data sets, additive models and backfitting methods are often used. A full Bayesian analysis for such models may include a large number of random effects, many of which are not intuitive, so researchers typically use noninformative improper or nearly improper priors...
متن کاملClustering in Additive Mixed Models with Approximate Dirichlet Process Mixtures using the EM Algorithm
SUMMARY: We consider additive mixed models for longitudinal data with a nonlinear time trend. As random effects distribution an approximate Dirichlet process mixture is proposed that is based on the truncated version of the stick breaking presentation of the Dirichlet process and provides a Gaussian mixture with a data driven choice of the number of mixture components. The main advantage of the...
متن کاملSpike-and-Slab Dirichlet Process Mixture Models
In this paper, Spike-and-Slab Dirichlet Process (SS-DP) priors are introduced and discussed for non-parametric Bayesian modeling and inference, especially in the mixture models context. Specifying a spike-and-slab base measure for DP priors combines the merits of Dirichlet process and spike-and-slab priors and serves as a flexible approach in Bayesian model selection and averaging. Computationa...
متن کاملBayesian semiparametric additive quantile regression
Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields po...
متن کامل