Abstract
In Sect. 5.1 we considered binary regression models, that is, regression situations where the response is observed in two categories. In many applications, from social science to medicine, response variables often have more than two categories. For example, consumers may choose between different brands of a product or they may express their opinion about some product in ordered categories ranging from “very satisfied” to “not satisfied at all.” Similarly, voters choose between several parties or they assess the quality of candidates in ordered categories. In medicine, we may, for example, not only distinguish between “infection” and “no infection” but also between several types of infection, as in Example 6.1 below.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsBibliography
Agresti, A. (2002). Categorical data analysis (2nd ed.). New York: Wiley.
Albert, J., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669–679.
Brezger, A., & Lang, S. (2006). Generalized additive regression based on Bayesian P-splines. Computational Statistics and Data Analysis, 50, 967–991.
Chen, M. H., & Dey, D. K. (2000). Bayesian analysis for correlated ordinal data models. In D. K. Dey, S. K. Ghosh, & B. K. Mallick (Eds.), Generalized linear models: A Bayesian perspective (pp. 133–159). New York: Marcel Dekker.
Fahrmeir, L., & Kaufmann, H. (1985). Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. The Annals of Statistics, 13, 342–368.
Fahrmeir, L., & Lang, S. (2001). Bayesian semiparametric regression analysis of multicategorical time-space data. Annals of the Institute of Statistical Mathematics, 53, 11–30.
Fahrmeir, L., & Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models (2nd ed.). Berlin: Springer.
Forthofer, R. N., & Lehnen, R. G. (1981). Public program analysis: A new categorical data approach. Belmont, CA: Lifetime Learning Publications.
Frühwirth-Schnatter, S., & Frühwirth, R. (2010). Data augmentation and MCMC for binary and multinomial logit models. In T. Kneib, & G. Tutz (Eds.), Statistical modelling and regression structures: Festschrift in honour of Ludwig Fahrmeir (pp. 111–132). Heidelberg: Springer.
Gamerman, D. (1997). Efficient sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing, 7, 57–68.
Holmes, C. C., & Held, L. (2006). Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis, 1, 145–168.
Imai, K., & van Dyk, D. A. (2005). A Bayesian analysis of the multinomial probit model using marginal data augmentation. Journal of Econometrics, 124, 311–334.
Lenk, P., & DeSarbo, W. (2000). Bayesian inference for finite mixtures of generalized linear models with random effects. Psychometrika, 65, 93–119.
McFadden, D. (1973). Conditional logit analysis of qualitative choice behaviour. In P. Zarembka (Ed.), Frontiers in Econometrics. New York: Academic.
McFadden, D. (1984). Econometric analysis of qualitative response models. In Z. Griliches, & M. Intriligator (Eds.), Handbook of econometrics (pp. 1395–1457). Amsterdam: North Holland.
Train, K. E. (2003). Discrete choice methods with simulation. Cambridge: Cambridge University Press.
Tutz, G. (2011). Regression for categorical data. Cambridge: Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fahrmeir, L., Kneib, T., Lang, S., Marx, B. (2013). Categorical Regression Models. In: Regression. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34333-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-34333-9_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34332-2
Online ISBN: 978-3-642-34333-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)