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:
“A general loathing of a gang or sect usually has some sound basis in instinct.”
—Ezra Pound (1885–1972)
“... if we look around us in social life and note down who are the faithful wives, the most patient and careful mothers, the most exemplary housekeepers, the model sisters, the wisest philanthropists, and the women of the most social influence, we will have to admit that most frequently they are women of cultivated minds, without which even warm hearts and good intentions are but partial influences.”
—Mrs. H. O. Ward (1824–1899)