ABSTRACT

Suppose that a binary response z, the two possible values of which are denoted by 0 and 1, has been observed from every statistical unit. The probabilities of “failure” (0) and “success” (1) of the statistical unit j are

Pr(zj = 0) = 1− ωj and Pr(zj = 1) = ωj ∀j = 1, . . . , N. Usually the success probability of the jth statistical unit is assumed to depend on the values (xj1, . . . , xjq) of the factors associated with the unit, that is,

Pr(zj = 1) = ωj = ω(xj1, . . . , xjq) ∀j = 1, . . . , N, where ω is a given function of factors x1, . . . , xq. Let there be n different combinations (xi1, . . . , xiq) ∀i = 1, . . . , n of values of factors and let there be mi and yi statistical units with the combination (xi1, . . . , xiq) of factors such that their observation was a success and failure, respectively. These units are said to form a covariate class.