On the conditioning problem in generalized linear models

Abstract

When weights are assigned to a data matrix, as in the iterative least squares estimator of a generalized linear model, the condition of the data matrix is changed. In this paper a geometrical approach to studying the mechanisms which determine the changed condition is introduced. Specifically, it is found that in some cases strong multicollinearities can be weakened or eliminated by the weights while in other cases the weights can induce an ill-conditioning.