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Journal of Applied Mathematics
Volume 2016 (2016), Article ID 1648462, 12 pages
Research Article

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

Department of Applied Mathematics, Nanjing Forestry University, Nanjing, Jiangsu 210037, China

Received 8 December 2015; Revised 23 February 2016; Accepted 2 March 2016

Academic Editor: Wei-Chiang Hong

Copyright © 2016 Ye-Mao Xia and Jian-Wei Gou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent variables and mixed observed responses. These models have been successfully applied to many different fields, including behavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments are constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model the distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through the simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For model selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are presented to illustrate the application of the methodology.