A GLM approach to quantal response models for mixtures

Quantal response models for the combination of two different stimuli are considered as exponential family regression models. In the most general cases the models are nonlinear in the sense that there is no link to a linear predictor. Examples include probit models for correlated independent action and logit models for similar action. Parameters for spontaneous response are included. An extensive series of examples shows that these models can be easily fitted to real data using standard statistical software. Results include deviance statistics for goodness of fit, as well as maximum likelihood estimates of EC50s, relative potencies, and mixing parameters, together with their standard deviations. Likelihood ratio statistics for testing special models are easily computed, facilitating the analysis of complex data sets. Deviance residuals help detect lack of fit and individual outliers.