MULTINOMIAL LOGISTIC REGRESSION ALGORITHM

DANKMAR BÖHNING

Department of Epidemiology, Free University Berlin, Augustastr. 37 1000 Berlin 45, Germany

(Received July 23, 1990; revised October 12, 1990)

Abstract. The lower bound principle (introduced in Böhning and Lindsay (1988, Ann. Inst. Statist. Math., 40, 641–663), Böhning (1989, Biometrika, 76, 375–383) consists of replacing the second derivative matrix by a global lower bound in the Loewner ordering. This bound is used in the Newton-Raphson iteration instead of the Hessian matrix leading to a monotonically converging sequence of iterates. Here, we apply this principle to the multinomial logistic regression model, where it becomes specifically attractive.

Key words and phrases: Kronecker product, Loewner ordering, lower bound principle, monotonicity.