Massey University, New Zealand - Institute of Information Sciences and Technology
Fisher made rapid progress with the development of linear models thanks to his facility with finite dimensional geometry, as described by Box in 1978. Linear statistical models thus have a geometric underpinning; the ANOVA table, for example, can be considered as a description of the vectors in an orthogonal breakup of the data vector.
In the literature there are two apparently distinct geometries described for loglinear models, one due to Fienberg in 1968 and the other to Haberman in 1974. These will be described, using a simple example.
This will lead to a description of two views of the geometry underlying generalised linear models. These two geometric approaches will be linked and related to the familiar geometry of linear models. For linear models, where the link function is the identity, the two geometries coalesce.
Finally, this geometric perspective will be used to develop a novel algorithm for fitting generalised linear models. Numerical comparison with the usual Newton-Raphson based algorithm will be made.