Generalized linear array model

In statistics, the generalized linear array model is used for analyzing the data sets with array structure. It based on the generalized linear model with the regression matrix written as a Kronecker product.

Overview

In the artcile published on Journal of Royal Statisitcal Society series B, 2006, Currie, Durban and Eiler introduced the generalized linear array model. Suppose the data set $\mathbf {Y}$ is arranged in a $d$-dimensional array with size $n_{1}\times n_{2}\times \ldots \times n_{d}$, thus, the corresponding data vector $\mathbf {y} ={\textbf {vec}}(\mathbf {Y} )$ with size $n_{1}n_{2}n_{3}\cdots n_{d}$, which can be analyzed with regression matrix $\mathbf {X} =\mathbf {X} _{d}\otimes \mathbf {X} _{d-1}\otimes \ldots \otimes \mathbf {X} _{1}$