Semiparametric Latent Variable Models With Bayesian P-Splines

• DOI: 10.1198/jcgs.2010.09094
• Publication Date: 2010-04-30T14:32:42Z
• Authors: Xin-Yuan Song; Zhao-Hua Lu
• Keywords: 0101 mathematics; 01 natural sciences

This article aims to develop a semiparametric latent variable model, in which outcome latent variables are related to explanatory latent variables and covariates through an additive structural equation formulated by a series of unspecified smooth functions. The Bayesian P-splines approach, together with a Markov chain Monte Carlo algorithm, is proposed to estimate smooth functions, unknown parameters, and latent variables in the model. The performance of the developed methodology is demonstrated by a simulation study. An illustrative example in analyzing bone mineral density in older men is provided. An Appendix which includes technical details of the proposed MCMC algorithm and an R code in implementing the algorithm are available as the online supplemental materials.