Abstract

Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining simple and easy-to-learn rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. The author includes both applied and theoretical discussions of the multivariate normal distribution, quadratic forms, maximum likelihood estimation, less than full rank models, and general mixed models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory.

• Provides a versatile format for investigating linear model theory, using the mean model
• Uses examples that are familiar to the student:
• Design of experiments, analysis of variance, regression, and normal distribution theory
• Includes a review of relevant linear algebra concepts
• Contains fully worked examples which follow the theorem/proof presentation

"At the theorectical level, this book deals with the general linear model: the usual results on the distribution of linear functions of the observations and of quadratic forms are all derived in the general case." --MATHEMATICAL REVIEWS

"This text presents the linear model (i.e., the analysis of variance and regression theory) from a sophisticated matrix algebra formulation. The book would be most suitable for graduate students of statistics who are already familiar with both linear algebra and the linear model." --JOURNAL OF MATHEMATICL PSYCHOLOGY