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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.