A NEW CLASS OF FLEXIBLE LINK FUNCTIONS WITH APPLICATION TO SPECIES CO-OCCURRENCE IN CAPE FLORISTIC REGION

摘要

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 skew- ness 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.