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linear model theory: univariate, multivariate, and mixed models
keith e. muller, paul w. stewart
Synopsis "linear model theory: univariate, multivariate, and mixed models"
statisticians often use linear models for data analysis, and for developing new statistical methods. a solid understanding of the underlying theory provides the foundation for success in either endeavor. historically, univariate, multivariate and mixed linear models have been discussed separately. in contrast, the authors sought a unified treatment in order to make clear the distinctions among the three classes of models. no single formulation proves uniformly best, therefore choosing the best approach requires a detailed knowledge of the differences and similarities. the authors believe that a student needs to acquire four sets of skills. 1. using all three classes of linear models correctly in practice requires knowing enough theory, especially a deep understanding of assumptions and their possible violations. however, the authors leave detailed discussions of diagnostics and data analyses to others. 2. correct use also requires knowing when to choose one type over another. 3. understanding the theory also helps guide when not to use any of the models. 4. finally, developing new methods requires a detailed knowledge of known work.
