ABSTRACT
This chapter aims to develop the multivariate general linear model, and examines the model parameters and general linear hypotheses. It also aims to extend the multivariate normal distribution to the matrix normal distribution and introduces the general multivariate linear mixed model. The chapter illustrates the general theory using examples in multivariate regression, multivariate analysis of variance, and multivariate analysis of covariance. It shows the relationship between univariate and multivariate analysis of repeated measurement data, and discusses how one may analyze extended linear hypotheses. Multivariate linear regression procedures are used in practice to explain variation in a vector of dependent variables by employing a set of independent variables using observational data. Regression methods may be applied using random dependent variables and several fixed predictors making few assumptions regarding the random errors: the classical multivariate linear regression model. Even though the parameter matrix is not unique, certain linear functions of the estimate are unique.
