On Link Selection in Generalized Linear Models
Generalized Linear Models (GLM) are extended to include the choice of a parametric link transformation family to improve fit over the standard GLM analysis in some data sets. However, the additional estimation of the link parameter results generally in higher estimated variances of the parameter estimates and numerical instability compared to the case when the correct link is known apriori. This paper extends two ideas developed for binary regression with parametric link (Czado ) — standardization and parameter orthogonality — to GLM’s aimed at reducing the variance inflation and numerical instability. Simple standardized link families for GLM’s are introduced and their usefulness are illustrated by an example.
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