If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax assumptions about Y and U.
If Y, B, and U were column vectors, the matrix equation above would represent multiple linear regression.
Thus, Yi is the ith observation of the dependent variable, Xik is kth observation of the kth independent variable, j = 1, 2, ..., p. The values βj represent parameters to be estimated, and εi is the ith independent identically distributed normal error.
The general linear model and the generalized linear model (GLM)[2][3] are two commonly used families of statistical methods to relate some number of continuous and/or categorical predictors to a single outcome variable.
The main difference between the two approaches is that the general linear model strictly assumes that the residuals will follow a conditionally normal distribution,[4] while the GLM loosens this assumption and allows for a variety of other distributions from the exponential family for the residuals.