Collinearity in generalized linear regression

Abstract

The problem of ill-conditioning in generalized linear regression is investigated. Besides collinearity among the explanatory variables, we define another type of ill-conditioning, namely ML-collinearity, which has similar detrimental effects on the covariance matrix, e.g. inflation of some of the estimated standard errors of the regression coefficients. For either situation there is collinearity among the columns of the matrix of the weighted variables. We present both methods to detect, as well as practical examples to illustrate, the difference between these two types of ill-conditioning. Also the applicability of alternative regression methods will be reviewed.

Keywords:

• Biased estimation
• Condition index
• Existence of ML estimates
• HI-conditioning
• Maximum likelihood estimator
• Collinearity

^*Biostatistical Centre, Department of Epidemiology, Catholic University Leuven, 3000 Leuven, Belgium

^†Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA 70803-5606, U.S.A.

^*Biostatistical Centre, Department of Epidemiology, Catholic University Leuven, 3000 Leuven, Belgium

^†Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA 70803-5606, U.S.A.

Notes

^*Biostatistical Centre, Department of Epidemiology, Catholic University Leuven, 3000 Leuven, Belgium

^†Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA 70803-5606, U.S.A.