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December 2013 A new class of flexible link functions with application to species co-occurrence in cape floristic region
Xun Jiang, Dipak K. Dey, Rachel Prunier, Adam M. Wilson, Kent E. Holsinger
Ann. Appl. Stat. 7(4): 2180-2204 (December 2013). DOI: 10.1214/13-AOAS663


Understanding the mechanisms that allow biological species to co-occur is of great interest to ecologists. Here we investigate the factors that influence co-occurrence of members of the genus Protea in the Cape Floristic Region of southwestern Africa, a global hot spot of biodiversity. Due to the binomial nature of our response, a critical issue is to choose appropriate link functions for the regression model. In this paper we propose a new family of flexible link functions for modeling binomial response data. By introducing a power parameter into the cumulative distribution function (c.d.f.) corresponding to a symmetric link function and its mirror reflection, greater flexibility in skewness can be achieved in both positive and negative directions. Through simulated data sets and analysis of the Protea co-occurrence data, we show that the proposed link function is quite flexible and performs better against link misspecification than standard link functions.


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Xun Jiang. Dipak K. Dey. Rachel Prunier. Adam M. Wilson. Kent E. Holsinger. "A new class of flexible link functions with application to species co-occurrence in cape floristic region." Ann. Appl. Stat. 7 (4) 2180 - 2204, December 2013.


Published: December 2013
First available in Project Euclid: 23 December 2013

zbMATH: 1283.62228
MathSciNet: MR3161718
Digital Object Identifier: 10.1214/13-AOAS663

Keywords: Bayesian method , community ecology , generalized linear model , MCMC , Model selection , symmetric power link function

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.7 • No. 4 • December 2013
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