ABSTRACT
In a designed experiment, the covariate vector usually comprises a number of indicator variables associated with blocking and treatment factors, together with quantitative information concerning various aspects of the experimental material. In observational studies, the vector of covariates consists of measured variables thought likely to influence the probability of a positive response. In constructing models for some data, one is normally interested in how the response probabilities are affected by the covariates rather than how the individuals are distributed over covariate classes. However, if the response probabilities are of interest, it is best to regard the marginal table of covariate class totals, m, as fixed, whether or not they were predetermined by design. Extrapolation beyond the range of the observed x-values in order to predict the probability of failure at extreme x-values is a hazardous exercise because its success depends heavily on the correctness of the assumed model, particularly on the choice of link function.
