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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 P-splines), 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.