A Bayesian method for analyzing combinations of continuous, ordinal, and nominal categorical data with missing values

Xiao Zhang, W. John Boscardin, Thomas R. Belin, Xiaohai Wan, Yulei He and Kui Zhang

Journal of Multivariate Analysis, 2015, vol. 135, issue C, 43-58

Abstract: From a Bayesian perspective, we propose a general method for analyzing a combination of continuous, ordinal (including binary), and categorical/nominal multivariate measures with missing values. We assume multivariate normal linear regression models for multivariate continuous measures, multivariate probit models for correlated ordinal measures, and multivariate multinomial probit models for multivariate categorical/nominal measures. Then we assume a multivariate normal linear model on the continuous vector comprised of continuous variables and those underlying normal variables for ordinal variables from multivariate probit models and for categorical variables from multinomial probit models. We develop a Markov chain Monte Carlo (MCMC) algorithm to estimate unknown parameters including regression parameters, cut-points for ordinal data from the multivariate probit models, and the covariance matrix encompassing both continuous variables and the underlying normal latent variables. Combining the continuous variables and the normal latent variables allows us to model combinations of continuous, ordinal, and categorical multivariate data simultaneously. The framework incorporates flexible priors for the covariance matrix, provides a foundation for inference about the underlying covariance structure, and imputes missing data where needed. The method is illustrated through simulated examples and two real data applications.

Keywords: Multivariate probit model; Multinomial probit model; MCMC (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X14002620
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:135:y:2015:i:c:p:43-58

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2014.11.007

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().