Reducing multi-collinearity in GLMS with categorical covariates

When dealing with GLMs with categorical covariates we show that varying the reference subclasses leads to different variance–covariance matrices and develop a relation between a measure of precision and a measure of multi-collinearity, by analysis and simulation. The net result is that we are able to demonstrate, inter alia, how to reduce multi-collinearity by a judicious choice of reference subclasses in GLMs with categorical covariates. We develop estimators for the discrete choice minima of our measures and evaluate their performance in a wide class of GLM structures likely to arise in practice.