A Bayesian Semiparametric Latent Variable Model for Mixed Responses |
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Authors: | Ludwig Fahrmeir Alexander Raach |
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Institution: | 1.Institut für Statistik, Seminar für Statistik und ihre Anwendung in den Wirtschafts- und Sozialwissenschaften,Ludwig-Maximilians-Universit?t München,Munich,Germany |
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Abstract: | In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects
on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing
LVMs with the usual linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates
and interactions with other covariates as well as spatial effects. Full Bayesian modelling is based on penalized spline and
Markov random field priors and is performed by computationally efficient Markov chain Monte Carlo (MCMC) methods. We apply
our approach to a German social science survey which motivated our methodological development.
We thank the editor and the referees for their constructive and helpful comments, leading to substantial improvements of a
first version, and Sven Steinert for computational assistance. Partial financial support from the SFB 386 “Statistical Analysis
of Discrete Structures” is also acknowledged. |
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Keywords: | latent variable models mixed responses penalized splines spatial effects MCMC |
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