The saddlepoint correction in conditional logistic likelihood analysis

Abstract

Barndorfi-Nielsen & Cox (1979) introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector. This approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states. It is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a noncentral hypergeometric random variable, discussed by Levin (1984) and Gart (1987), while providing analogous formulae in more general cases; and extends, to the general case, an algorithm of McCullagh (1984) for the approximate calculation of conditional maximum likelihood estimates of log odds ratio regression coefficients from several fourfold tables.