Bayesian dynamic modeling of latent trait distributions.

Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.

[1]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[2]  T. Ferguson.  Prior Distributions on Spaces of Probability Measures , 1974 .

[3]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[4]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[5]  M. West.  On scale mixtures of normal distributions , 1987 .

[6]  M. West,et al.  Hyperparameter estimation in Dirichlet process mixture models , 1992 .

[7]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[8]  S. MacEachern.  Estimating normal means with a conjugate style dirichlet process prior , 1994 .

[9]  M. Lavine.  On an approximate likelihood for quantiles , 1995 .

[10]  S. MacEachern,et al.  A semiparametric Bayesian model for randomised block designs , 1996 .

[11]  A. Gelfand,et al.  Dirichlet Process Mixed Generalized Linear Models , 1997 .

[12]  L. Ryan,et al.  Latent Variable Models for Mixed Discrete and Continuous Outcomes , 1997 .

[13]  J G Ibrahim,et al.  A semiparametric Bayesian approach to the random effects model. , 1998, Biometrics.

[14]  D. Reboussin,et al.  Estimating Equations for a Latent Transit ion Model with Multiple Discrete Indicators , 1999, Biometrics.

[15]  Jim Albert,et al.  Ordinal Data Modeling , 2000 .

[16]  Xihong Lin,et al.  Latent Variable Models for Longitudinal Data with Multiple Continuous Outcomes , 2000, Biometrics.

[17]  D. Dunson,et al.  Bayesian latent variable models for clustered mixed outcomes , 2000 .

[18]  Radford M. Neal.  Markov Chain Sampling Methods for Dirichlet Process Mixture Models , 2000 .

[19]  M. Steel,et al.  BAYESIAN REGRESSION ANALYSIS WITH SCALE MIXTURES OF NORMALS , 2000, Econometric Theory.

[20]  M. Escobar,et al.  Markov Chain Sampling Methods for Dirichlet Process Mixture Models , 2000 .

[21]  M. Knott,et al.  Generalized latent trait models , 2000 .

[22]  A. Gelfand,et al.  Bayesian Semiparametric Median Regression Modeling , 2001 .

[23]  A. Utsugi,et al.  Bayesian Analysis of Mixtures of Factor Analyzers , 2001, Neural Computation.

[24]  S Y Lee,et al.  Latent variable models with mixed continuous and polytomous data , 2001, Biometrics.

[25]  S L Zeger,et al.  The Evaluation of Multiple Surrogate Endpoints , 2001, Biometrics.

[26]  Jian Qing Shi,et al.  Maximum Likelihood Estimation of Two‐Level Latent Variable Models with Mixed Continuous and Polytomous Data , 2001 .

[27]  Alan E. Gelfand,et al.  A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models , 2002 .

[28]  Glen Takahara,et al.  Independent and Identically Distributed Monte Carlo Algorithms for Semiparametric Linear Mixed Models , 2002 .

[29]  Lancelot F. James,et al.  Approximate Dirichlet Process Computing in Finite Normal Mixtures , 2002 .

[30]  Jason Roy,et al.  Analysis of Multivariate Longitudinal Outcomes With Nonignorable Dropouts and Missing Covariates , 2002 .

[31]  Louise Ryan,et al.  EFFECTS OF COVARIANCE MISSPECIFICATION IN A LATENT VARIABLE MODEL FOR MULTIPLE OUTCOMES , 2002 .

[32]  Geoffrey J. McLachlan,et al.  Modelling high-dimensional data by mixtures of factor analyzers , 2003, Comput. Stat. Data Anal..

[33]  Diana L Miglioretti,et al.  Latent transition regression for mixed outcomes. , 2003, Biometrics.

[34]  Peter Müller,et al.  ANOVA DDP Models: A Review , 2003 .

[35]  Jack A. Taylor,et al.  Bayesian Latent Variable Models for Median Regression on Multiple Outcomes , 2003, Biometrics.

[36]  David D. Denison,et al.  Nonlinear estimation and classification , 2003 .

[37]  D. Dunson.  Dynamic Latent Trait Models for Multidimensional Longitudinal Data , 2003 .

[38]  Jason Roy,et al.  Scaled marginal models for multiple continuous outcomes. , 2003, Biostatistics.

[39]  Fernando A. Quintana,et al.  Nonparametric Bayesian data analysis , 2004 .

[40]  S. MacEachern,et al.  An ANOVA Model for Dependent Random Measures , 2004 .

[41]  P. Müller,et al.  A method for combining inference across related nonparametric Bayesian models , 2004 .

[42]  Michael A. West,et al.  BAYESIAN MODEL ASSESSMENT IN FACTOR ANALYSIS , 2004 .

[43]  D. M. Titterington,et al.  Mixtures of Factor Analysers. Bayesian Estimation and Inference by Stochastic Simulation , 2004, Machine Learning.

[44]  S. MacEachern,et al.  Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing , 2005 .

[45]  J. E. Griffin,et al.  Order-Based Dependent Dirichlet Processes , 2006 .

[46]  Michael A. West,et al.  Hierarchical priors and mixture models, with applications in regression and density estimation , 2006 .