This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models
A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding.
The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
Table of Contents
A Review of Vector and Matrix Algebra. Properties of Special Matrices. Generalized Inverse and Solutions to Linear Systems. The General Linear Model. Multivariate Normal And Related Distributions. Sampling From the Multivariate Normal Distribution. Inference for the General Linear Model. Multiple Regression Models.. Fixed Effects Linear Models. Random Effects and Mixed-Effects Models. Special Topics. Appendix.
Nalini Ravishanker, Dipak K. Dey