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A Bayesian Semiparametric Latent Variable Model for Mixed Responses

Published online by Cambridge University Press:  01 January 2025

Ludwig Fahrmeir  and
Alexander Raach
Ludwig Fahrmeir*
Affiliation:
Ludwig-Maximilians-Universität München
Alexander Raach
Affiliation:
Ludwig-Maximilians-Universität München
*
Requests for reprints should be sent to Ludwig Fahrmeir, Institut für Statistik, Seminar für Statistik und ihre Anwendung in den Wirtschafts- und Sozialwissenschaften, Ludwig-Maximilians-Universität München, Ludwigstraße 33, 80539 Munich, Germany. E-mail: ludwig.fahrmeir@stat.uni-muenchen.de
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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.

Keywords

latent variable modelsmixed responsespenalized splinesspatial effectsMCMC

Information

Type
Theory and Methods
Information
Psychometrika , Volume 72 , Issue 3 , September 2007 , pp. 327 - 346
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

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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