Modeling Associations Among Multivariate Longitudinal Categorical Variables in Survey Data: A Semiparametric Bayesian Approach

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the distributions of the factors are modeled nonparametrically through a dynamic hierarchical Dirichlet process prior. A Markov chain Monte Carlo algorithm is developed for fitting the model, and the methodology is exemplified through a study of the dynamics of public attitudes toward science and technology in the United States over the period 1992–2001.

[1]  B. Escofier,et al.  Analyses factorielles simples et multiples : objectifs, méthodes et interprétation , 2008 .

[2]  Paul F. Lazarsfeld,et al.  Latent Structure Analysis. , 1969 .

[3]  M. Greenacre.  Correspondence analysis in practice , 1993 .

[4]  S. MacEachern.  Decision Theoretic Aspects of Dependent Nonparametric Processes , 2000 .

[5]  Leo A. Goodman,et al.  Some Useful Extensions of the Usual Correspondence Analysis Approach and the Usual Log-Linear Models Approach in the Analysis of Contingency Tables , 1986 .

[6]  D. Dunson.  Bayesian dynamic modeling of latent trait distributions. , 2006, Biostatistics.

[7]  J. Q. Smith,et al.  1. Bayesian Statistics 4 , 1993 .

[8]  Robert J. Mislevy,et al.  Recent Developments in the Factor Analysis of Categorical Variables , 1986 .

[9]  J. Tukey,et al.  Multiple-Factor Analysis , 1947 .

[10]  L. A. Goodman.  [Some Useful Extensions of the Usual Correspondence Analysis Approach and the Usual Log-Linear Models Approach in the Analysis of Contingency Tables]: Reply to Discussion , 1986 .

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

[12]  D. Dunson,et al.  Bayesian Semiparametric Structural Equation Models with Latent Variables , 2010 .

[13]  L. A. Goodman.  Exploratory latent structure analysis using both identifiable and unidentifiable models , 1974 .

[14]  Michael I. Jordan,et al.  Hierarchical Dirichlet Processes , 2006 .

[15]  John Bibby,et al.  The Analysis of Contingency Tables , 1978 .

[16]  Serena Ng,et al.  A Hierarchical Factor Analysis of U.S. Housing Market Dynamics , 2011 .

[17]  Sik-Yum Lee,et al.  Bayesian Selection on the Number of Factors in a Factor Analysis Model , 2002 .

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

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

[20]  Lancelot F. James,et al.  Gibbs Sampling Methods for Stick-Breaking Priors , 2001 .

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

[22]  D. Dunson,et al.  Sparse Bayesian infinite factor models. , 2011, Biometrika.

[23]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[24]  David B Dunson,et al.  Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis , 2009, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[25]  Tatsuzo Suzuki,et al.  DIMENSIONS OF PUBLIC ACCEPTANCE OF SCIENCE AND TECHNOLOGY AMONG FIVE INDUSTRIALIZED NATIONS , 1991 .

[26]  Neil Henry.  Latent structure analysis , 1969 .

[27]  David B. Dunson,et al.  The dynamic hierarchical Dirichlet process , 2008, ICML '08.

[28]  R. Tsay,et al.  Quantile Regression Models with Factor-Augmented Predictors and Information Criterion , 2011 .

[29]  Leo A. Goodman,et al.  5. Statistical Methods and Graphical Displays for Analyzing how the Association between Two Qualitative Variables Differs among Countries, among Groups, or over Time: A Modified Regression-Type Approach , 1998 .

[30]  Richard F. Muth,et al.  Housing market dynamics , 1988 .

[31]  Hee-Je Bak,et al.  Education and Public Attitudes toward Science: Implications for the "Deficit Model" of Education and Support for Science and Technology , 2001 .