Scaled link functions and generalized likelihood inferences for heterogeneous binary response data

This paper describes binary regression models in which the link function has scale param­eters that may be estimated along with the regression parameters. One motivation is to provide a plausible model for group binary responses. In this case a natural class of scale functions is obtained by treating the group responses as thresholded averages of possibly correlated latent variables. The latent variables represent individual responses within the group. Scaled link functions also arise naturally if the latent response variables are het­eroscedastic. We develop generalized likelihood ratio inferences in case the observed binary responses are themselves correh1ted. Group response data from environmental toxicology illustrate the scaled link function analysis.