ABSTRACT
The development of models for binary and binomial response data was originally prompted by the needs of a type of experimental investigation known as a biological assay, or bioassay for short. In a typical assay, different concentrations of a chemical compound are applied to batches of experimental animals. The number of animals in each batch that respond to the chemical is then recorded, and these values are regarded as observations on a binomial response variable. In this application area, models based on the logistic and probit transformations can be motivated through the notion of a tolerance distribution. This is described in Section 4.1. Some specific aspects of bioassay are discussed in Sections 4.2-4.4, and the extension from linear to non-linear logistic modelling is considered in Section 4.5. A transformation of the binary response probability that is not as widely used as the logistic or probit transformations is the complementary log-log transformation. Nevertheless, models based on this transformation do arise naturally in a number of areas of application, some of which are described in Section 4.6.
