The general linear model (GLM) is a statistical linear model. It may be written as
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 errors or noise. The errors are usually assumed to follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax assumptions about Y and U.
The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression model to the case of more than one dependent variable. If Y, B, and U were column vectors, the matrix equation above would represent multiple linear regression.
Hypothesis tests with the general linear model can be made in two ways: multivariate or as several independent univariate tests. In multivariate tests the columns of Y are tested together, whereas in univariate tests the columns of Y are tested independently, i.e., as multiple univariate tests with the same design matrix.
Read more about General Linear Model: Multiple Linear Regression, Applications
Famous quotes containing the words general and/or model:
“In the drawing room [of the Queen’s palace] hung a Venus and Cupid by Michaelangelo, in which, instead of a bit of drapery, the painter has placed Cupid’s foot between Venus’s thighs. Queen Caroline asked General Guise, an old connoisseur, if it was not a very fine piece? He replied “Madam, the painter was a fool, for he has placed the foot where the hand should be.””
—Horace Walpole (1717–1797)
“Socrates, who was a perfect model in all great qualities, ... hit on a body and face so ugly and so incongruous with the beauty of his soul, he who was so madly in love with beauty.”
—Michel de Montaigne (1533–1592)