Inference in linear models
T. W. Anderson · Lecture notes-monograph series · 1994
A general linear model can be written as Y = XB 1 + U, where Y^ is an N X p matrix of observable dependent variables, X is an N X q matrix of independent variables, B 1 is a q X p matrix of parameters, and U is an N X p matrix of unobservable random variables.The elements of X may be observable or alternatively unobservable (that is, latent); they may be nonstochastic or stochastic.The model includes regression, linear functional and structural relations, multivariate analysis of variance, factor analysis, and some simultaneous equations models.This paper considers the relationships between various models and presents methods of estimating the parameters under various conditions. Testing hypotheses about the rank of XB 1(the dimensionality of the latent variables when X is not observed) are also treated.