Logit, Probit, and Other Response Functions

A general statistical problem is to model a binomial probability in terms of a vector of explanatory variables. We observe independent responsesy ₁, …,y_N , wherey_i is assumed binomial with sample sizen_i and probability of successp_i . (In the special case where the4sample sizesn_i = ⋯ =n_N = 1, we have Bernoulli observations.) Corresponding to theith observation, we also observek covariatesx _i1,…,x_ik ; we letx_i = (x _i1,…,x_ik ) denote the vector of covariates. We relate the binomial probabilities with the covariates by means of the equation (1.1) g ( p i ) = x i β, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119144/ecefbed9-1426-4c02-8a80-78b939a7d44e/content/eq1_v2.tif"/>