Parametric Links

Parametric Links for Binary Response Models
Roger Koenker and Jungmo Yoon

The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are suggested: the Gosset link based on the Student t latent variable model with the degrees of freedom parameter controlling the tail behavior, and the Pregibon link based on the (generalized) Tukey $\lambda$ family with two shape parameters controlling skewness and tail behavior. Both Bayesian and maximum likelihood methods for estimation and inference are explored. Implementations of the methods are illustrated in the R environment.

The paper is available in pdf.

There is also a brief note submitted to Rnews describing the implementation available in pdf. A compressed tarball of the code used for the Rnews article can also be downloaded.

Comments are, of course, always welcome.