GENERALIZED BILINEAR REGRESSION

This paper discusses the application of generalised linear methods to bilinear models by criss-cross regression. It proposes an extension to segmented bilinear models in which the expectation matrix is linked t o a sum in which each segment has specified row and column covariance matrices as well as a coefficient parameter matrix that is specified o nly by its rank. This extension includes a variety of biadditive model s including the generalised Tukey degree of freedom for non-additivity model that consists of two bilinear segments, one of which is constan t. The extension also covers a variety of other models for which least squares fits had not hitherto been available, such as higher-way layo uts combined into the rows and columns of a matrix, and a harmonic mod el which can be reparameterised so a lower rank fit is equivalent to a constant phase parameter. A number of practical applications are prov ided,including displaying fits by biplots and using them to diagnose m odels.