ABSTRACT
A general statistical problem is to model a binomial probability in terms of a vector of explanatory variables. We observe independent responses y 1, …, yN , where yi is assumed binomial with sample size ni and probability of success pi . (In the special case where the 4sample sizes ni = ⋯ = nN = 1, we have Bernoulli observations.) Corresponding to the ith observation, we also observe k covariates x i1, …, xik ; we let x i = (x i1, …, xik ) denote the vector of covariates. We relate the binomial probabilities with the covariates by means of the equation g ( p i ) = x i β , https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315373645/31b853cf-6b50-4d97-8c4f-c365935dd1f7/content/equ1_1.tif"/>
