Generalized extreme value regression for ordinal response data |
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| Authors: | Xia Wang Dipak K Dey |
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| Institution: | (1) Connecticut River Coastal Conservation District, Inc., 27 Washington Street, Middletown, CT 06457, USA;(2) Department of Ecology and Evolutionary Biology, University of Connecticut, 75 North Eagleville Road, Unit 3043, Storrs, CT, USA;(3) Department of Plant Sciences, University of California, One Shields Avenue, Davis, CA 95616, USA; |
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| Abstract: | This paper introduces a flexible skewed link function for modeling ordinal response data with covariates based on the generalized
extreme value (GEV) distribution. Commonly used probit, logit and complementary log-log links are prone to link misspecification
because of their fixed skewness. The GEV link is flexible in fitting the skewness in the response curve with a free shape
parameter. Using Bayesian methodology, it automatically detects the skewness in the response curve along with the model fitting.
The flexibility of the proposed model is illustrated by its application to an ecological survey data about the coverage of
Berberis thunbergii in New England. We employ the latent variable approach by Albert and Chib (J Am Stat Assoc 88:669–679, (1993) to develop
computational schemes. For model selection, we employ the Deviance Information Criterion (DIC). |
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