The general linear model (GLM) provides a general framework for a large set of models whose common goal is to explain or predict a quantitative dependent variable by a set of independent variables that can be categorical or quantitative. The GLM encompasses techniques such as Student's t test, simple and multiple linear regression, analysis of variance, and covariance analysis. The GLM is adequate only for fixed-effect models. In order to take into account random-effect models, the GLM needs to be extended and becomes the mixed-effect model.
Vectors are denoted with boldface lower-case letters (e.g., y), and matrices are denoted with boldface upper-case letters (e.g., X). The transpose of a matrix is denoted by the superscriptT, and the inverse of a matrix is denoted by the superscript–1. ...
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