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MULTINOMIAL LOGISTIC REGRESSION ALGORITHM

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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.

**Source**
( TeX ,
DVI ,
PS )