Generalized Linear Array Model - Overview

Overview

The generalized linear array model or GLAM was introduced in 2006. Such models provide a structure and a computational procedure for fitting generalized linear models or GLMs whose model matrix can be written as a Kronecker product and whose data can be written as an array. In a large GLM, the GLAM approach gives very substantial savings in both storage and computational time over the usual GLM algorithm.

Suppose that the data is arranged in a -dimensional array with size ; thus,the corresponding data vector has size . Suppose also that the design matrix is of the form

The standard analysis of a GLM with data vector and design matrix proceeds by repeated evaluation of the scoring algorithm

where represents the approximate solution of, and is the improved value of it; is the diagonal weight matrix with elements

and

is the working variable.

Computationally, GLAM provides array algorithms to calculate the linear predictor,

and the weighted inner product

without evaluation of the model matrix