A new class of flexible link functions with application to species co-occurrence in cape floristic region
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2014
- DOI:
- 10.48550/arXiv.1401.1915
- arXiv:
- arXiv:1401.1915
- Bibcode:
- 2014arXiv1401.1915J
- Keywords:
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- Statistics - Applications
- E-Print:
- Published in at http://dx.doi.org/10.1214/13-AOAS663 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)