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2009-Linear Model Methodology1.pdf
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Chapman & Hall/CRC | 2009 | ISBN: 1584884819 | 562 pages | PDF | 2,9 MB
Given the importance of linear models in statistical theory and experimental research,a good understanding of their fundamental principles and theory isessential. Supported by a large number of examples, Linear ModelMethodology provides a strong foundation in the theory of linear modelsand explores the latest developments in data analysis. After presentingthe historical evolution of certain methods and techniques used inlinear models, the book reviewsvector spaces and linear transformations and discusses the basicconcepts and results of matrix algebra that are relevant to the studyof linear models. Although mainly focused on classical linear models,the next several chapters also explore recent techniques for solvingwell-known problems that pertain to the distribution and independenceof quadratic forms, the analysis of estimable linear functions andcontrasts, and the general treatment of balanced random andmixed-effects models. The author then covers more contemporary topicsin linear models, including the adequacy of Satterthwaite’sapproximation, unbalanced fixed- and mixed-effects models,heteroscedastic linear models, response surface models with randomeffects, and linear multiresponse models. The final chapter introducesgeneralized linear models, which represent an extension of classicallinear models. Linear models provide the groundwork for analysis ofvariance, regression analysis, response surface methodology, variancecomponents analysis, and more, making it necessary to understand thetheory behind linear modeling. Reflecting advances made in the lastthirty years, this book offers a rigorous development of the theoryunderlying linear models.
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