A CONTINUUM OF PRINCIPAL COMPONENT GENERALIZED LINEAR REGRESSIONS

The motivation of the paper is to present an option to maximum likelihood estimation when the information matrix is ill-conditioned. The impacts and diagnosis of ill-conditioned information are revisited. We combine ideas from Good and Smith [41 and Marx and Smith [10] to develop a class of principal component estimators, for generalized linear regression, defined by a scaling parameter. The additional parameter allows a spectrum of standardized explanatory variables which can yield interpolation between correlation and covariance matrices. We show that choice of the scaling parameter depends on the researcher's objectives for the model. A unit scaling parameter produces results of Marx and Smith [10]. If further restrictions of normal response data and the identity link function are imposed with an unit scaling parameter, we have traditional principal component multiple regression (Webster et al. [16]). We discuss the appropriateness of principal component regression. An illustrative example using Poisson response data and the log link function demonstrates the usefulness of the scaling parameter for a generalized linear regression with severely ill-conditioned information.