Chemistry - General linear model

The general linear model (GLM) is a statistical, linear model. It may be written as

$\mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{U},$

where Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing residuals (i.e., errors or noise). The residual is usually assumed to follow a multivariate normal distribution.

The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA , ordinary linear regression, "t-test" and "F-test".

Hypothesis tests with the general linear model can be made in two ways: multivariate and mass-univariate.

Applications

An application of the general linear model appears in the analysis of neuroimages where Y contains data from brain scanners, X contains experimental design variables and confounds. It is usually tested in a mass-univariate way and is often referred to as statistical parametric mapping.