Raach, Alexander (2006): A Bayesian semiparametric latent variable model for binary, ordinal and continuous response. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics 

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Abstract
This thesis discusses a latent variable model (LVM) which is based on a Bayesian approach and is estimated by Markov chain Monte Carlo methods (MCMC). The model extends classic factor analysis by allowing not only for gaussian metric manifest variables, but also for binary and ordinal indicators which are very common in many areas of application (e.g. psychology, sociology). Furthermore, a semiparametric predictor is introduced which describes the influence of covariates on the latent variables. The predictor may contain parametric effects, smooth functions of metric covariates (modeled by random walks and Psplines), spatial effects (modeled by Markov random fields) and interactions of metric and categorical covariates. The integration of temporal effects is easily possible. Consequently, the influence of covariates on the latent variables can be analyzed in much more detail than with currently available methods. One emphasis of this work is the development of an efficient MCMC algorithm with good estimation properties (in particular concerning the cutpoints of ordinal indicators) and its implementation in the standard software package R. Another focus lies on the demonstration of the model's applicability using data from an internet survey. Several models with differently structured predictors are analyzed and first ideas for model selection are presented.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Latent variable models, mixed responses, penalized splines, spatial effects, MCMC 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  26. January 2006 
1. Referee:  Fahrmeir, Ludwig 
Persistent Identifier (URN):  urn:nbn:de:bvb:1948301 
MD5 Checksum of the PDFfile:  819f9fb7df99ca795752f2cf2c45ea07 
Signature of the printed copy:  0001/UMC 15152 
ID Code:  4830 
Deposited On:  07. Feb 2006 
Last Modified:  16. Oct 2012 07:55 