A new class of flexible link functions with application to species co-occurrence in Cape Floristic Region

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.