Ronald Christensen – författare

Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Second Edition presents linear structures for modeling data with an emphasis on how to incorporate specific ideas (hypotheses) about the structure of the data into a linear model for the data. The book carefully analyzes small data sets by using tools that are easily scaled to big data. The tools also apply to small relevant data sets that are extracted from big data.

New to the Second Edition

The text can be used in a variety of courses, including a yearlong graduate course on regression and ANOVA or a data analysis course for upper-division statistics students and graduate students from other fields. It places a strong emphasis on interpreting the range of computer output encountered when dealing with unbalanced data.

This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author''s emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes a more extensive discussion of best prediction and associated ideas of R2, as well as new sections on inner products and perpendicular projections for more general spaces and Milliken and Graybill’s generalization of Tukey’s one degree of freedom for nonadditivity test.

Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Second Edition presents linear structures for modeling data with an emphasis on how to incorporate specific ideas (hypotheses) about the structure of the data into a linear model for the data. The book carefully analyzes small data sets by using tools that are easily scaled to big data. The tools also apply to small relevant data sets that are extracted from big data.

New to the Second Edition

The text can be used in a variety of courses, including a yearlong graduate course on regression and ANOVA or a data analysis course for upper-division statistics students and graduate students from other fields. It places a strong emphasis on interpreting the range of computer output encountered when dealing with unbalanced data.

This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author''s emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models.  In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman''s critique of the sandwich estimator, and much more.

This book examines statistical models for frequency data.  The primary focus is on log-linear models for contingency tables but also includes extensive discussion of logistic regression.  Topics such as logistic discrimination, generalized linear models, and correspondence analysis are also explored.

The treatment is designed for readers with prior knowledge of analysis of variance and regression.  It builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data.  While emphasizing similarities between methods for discrete and continuous data, this book also carefully examines the differences in model interpretations and evaluation that occur due to the discrete nature of the data.  Numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises.  A major addition to the third edition is the availability of a companion online manual providing R code for the procedures illustrated in the book.

The book begins with an extensive discussion of odds and odds ratios as well as concrete illustrations of basic independence models for contingency tables.  After developing a sound applied and theoretical basis for frequency models analogous to ANOVA and regression, the book presents, for contingency tables, detailed discussions of the use of graphical models, of model selection procedures, and of models with quantitative factors.  It then explores generalized linear models, after which all the fundamental results are reexamined using powerful matrix methods.  The book then gives an extensive treatment of Bayesian procedures for analyzing logistic regression and other regression models for binomial data.  Bayesian methods are conceptually simple and unlike traditional methods allow accurate conclusions to be drawn without requiring large sample sizes.  The book concludes with two new chapters: one on exact conditional tests for small sample sizes and another on the graphical procedure known as correspondence analysis.