Linear Models: An Integrated Approach aims to provide a clear and deep understanding of the general linear model using simple statistical ideas. Elegant geometric arguments are also invoked as needed and a review of vector spaces and matrices is provided to make the treatment self-contained. Complex, matrix-algebraic methods, such as those used in the rank-deficient case, are replaced by statistical proofs that are more transparent and that show the parallels with the simple linear model.
This book has the following special features:
o Use of simple statistical ideas such as linear zero functions and covariance adjustment to explain the fundamental as well as advanced concepts
o Emphasis on the statistical interpretation of complex algebraic results
o A thorough treatment of the singular linear model, including the case of multivariate response
o A unified discussion on models with a partially unknown dispersion matrix, including mixed-effects/variance-components models and models for spatial and time series data
o Insight into updates on the linear model and their connection with diagnostics, design, variable selection, the Kalman filter, etc.
o An extensive discussion on the foundations of linear inference, along with linear alternatives to least squares
o Coverage of other special topics, such as collinearity, stochastic and inequality constraints, misspecified models, etc.
o Simpler proofs of numerous known results
o Pointers to current research through examples and exercises
