In statistics, the generalized linear array model (GLAM) is used for analyzing data sets with array structures. It based on the generalized linear model with the design matrix written as a Kronecker product.

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 also that the design matrix is of the form

proceeds by repeated evaluation of the scoring algorithm

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

Example

given by

.

is the example of Face-splitting product of matrices, which was proposed by Vadym Slyusar in 1996:

means Face-splitting product.

-dimensions.

Applications

one-dimensional smoothing matrices.

References