Abstract
We present a unified semiparametric Bayesian approach based on Markov random field priors for analyzing the dependence of multicategorical response variables on time, space and further covariates. The general model extends dynamic, or state space, models for categorical time series and longitudinal data by including spatial effects as well as nonlinear effects of metrical covariates in flexible semiparametric form. Trend and seasonal components, different types of covariates and spatial effects are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference is fully Bayesian and uses MCMC techniques for posterior analysis. The approach in this paper is based on latent semiparametric utility models and is particularly useful for probit models. The methods are illustrated by applications to unemployment data and a forest damage survey.
Similar content being viewed by others
References
Albert, J. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data, J. Amer. Statist. Assoc., 88, 669-679.
Besag, J., York, J. and Mollie, A. (1991). Bayesian image restoration with two applications in spatial statistics (with discussion), Ann. Inst. Statist. Math., 43, 1-59.
Chen, M. H. and Dey, D. K. (2000). Bayesian analysis for correlated ordinal data models, Generalized Linear Models: A Bayesian Perspective (eds. D. K. Dey, S. K. Ghosh and B. K. Mallick), Chapter 8, 133-159, Marcel, New York.
Clayton, D. (1996). Generalized linear mixed models, Markov Chain Monte Carlo in Practice, (eds. Gilks, W., Richardson S. and Spiegelhalter D), 275-301, Chapman and Hall, London.
Fahrmeir, L. and Lang, S. (2000). Bayesian semiparametric regression analysis of multicategorical time-space data, Proceedings of the International Symposium on Frontiers of Time Series Modeling, Tokyo, 82-91.
Fahrmeir, L. and Lang, S. (2001). Bayesian inference for generalized additive mixed models based on Markov random field priors, Applied Statistics (to appear).
Fahrmeir, L. and Tutz, G. (2001). Multivariate Statistical Modelling based on Generalized Linear Models, 2nd ed., Springer, New York.
Göttlein, A. and Pruscha, H. (1996). Der Einfluss von Bestandskenngrössen, Topographie, Standort und Witterung auf die Entwicklung des Kronenzustandes im Bereich des Forstamtes Rothenbuch, Forstwissenschaftliches Centralblatt, 114, 146-162.
Knorr-Held, L. (1999). Conditional prior proposals in dynamic models, Scand. J. Statist., 26, 129-144.
Knorr-Held, L. (2000). Bayesian modelling of inseparable space-time variation in disease risk, Statistics in Medicine, 19, 2555-2567.
Knorr-Held, L. and Besag, J. (1998). Modelling risk from a desease in time and space, Statistics and Medicine, 17, 2045-2060.
Lang, S. and Brezger, A. (2000). BayesX—Software for Bayesian inference based on Markov chain Monte Carlo simulation techniques, Discussion Paper 187, Sonderforschungsbereich 386, Ludwigs-Maximilians-Universität München.
Lang, S. and Fahrmeir, L. (2001). Bayesian generalized additive mixed models. A simulation study, Discussion paper 230, Sonderforschungsbereich 386, Ludwigs-Maximilians-Universität München.
Rue, H. (2000). Fast sampling of Gaussian Markov random fields with applications, Tech. Report, No. 1/2000, Norwegian University of Science and Technology, Trondheim, Norway.
Yau, P., Kohn, R. and Wood, S. (2000). Bayesian variable selection and model averaging in high dimensional multinomial nonparametric regression, University of New South Wales (Preprint).
Author information
Authors and Affiliations
About this article
Cite this article
Fahrmeir, L., Lang, S. Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data. Annals of the Institute of Statistical Mathematics 53, 11–30 (2001). https://doi.org/10.1023/A:1017904118167
Issue Date:
DOI: https://doi.org/10.1023/A:1017904118167