Analysis of variance, design, and regression: linear modeling for unbalanced data

632 Pages·2016·4.061 MB·English

by  Christensen, Ronald

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

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New to the Second Edition f and Regression

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• Reorganized to focus on unbalanced data
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• Reworked balanced analyses using methods for unbalanced data r
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• Introductions to nonparametric and lasso regression
n Linear Modeling for
• Introductions to general additive and generalized additive models c
• Examination of homologous factors e
, Unbalanced Data

• Unbalanced split plot analyses D
• Extensions to generalized linear models e
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• R, Minitab®, and SAS codes on the author’s website
i Second Edition
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The text can be used in a variety of courses, including a yearlong graduate course n
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on regression and ANOVA or a data analysis course for upper-division statistics a
students and graduate students from other fields. It places a strong emphasis n
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on interpreting the range of computer output encountered when dealing with

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unbalanced data.
e
g
Ronald Christensen is a professor of statistics in the Department of Mathematics
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and Statistics at the University of New Mexico. Dr. Christensen is a fellow of the
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American Statistical Association (ASA) and Institute of Mathematical Statistics. He s
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is a past editor of The American Statistician and a past chair of the ASA’s Section o
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on Bayesian Statistical Science. His research interests include linear models,
Bayesian inference, log-linear and logistic models, and statistical methods.
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s Ronald Christensen
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K26114
www.crcpress.com
K26114_cover.indd 1 11/9/15 2:22 PM
Analysis of
Variance, Design,
and Regression
Linear Modeling for
Unbalanced Data
Second Edition
CHAPMAN & HALL/CRC
Texts in Statistical Science Series
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Francesca Dominici, Harvard School of Public Health, USA
Julian J. Faraway, University of Bath, UK
Martin Tanner, Northwestern University, USA
Jim Zidek, University of British Columbia, Canada
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Texts in Statistical Science
Analysis of
Variance, Design,
and Regression
Linear Modeling for
Unbalanced Data
Second Edition
Ronald Christensen
University of New Mexico
Albuquerque, USA
CRC Press
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To Mark, Karl, and John
It was great fun.

Contents
Preface xvii
EditedPrefacetoFirstEdition xxi
Computing xxv
1 Introduction 1
1.1 Probability 1
1.2 Randomvariablesandexpectations 4
1.2.1 Expectedvaluesandvariances 6
1.2.2 Chebyshev’sinequality 9
1.2.3 Covariancesandcorrelations 10
1.2.4 Rulesforexpectedvaluesandvariances 12
1.3 Continuousdistributions 13
1.4 Thebinomialdistribution 17
1.4.1 Poissonsampling 21
1.5 Themultinomialdistribution 21
1.5.1 IndependentPoissonsandmultinomials 23
1.6 Exercises 24
2 OneSample 27
2.1 Exampleandintroduction 27
2.2 Parametricinferenceaboutμ 31
2.2.1 Significancetests 34
2.2.2 Confidenceintervals 37
2.2.3 Pvalues 38
2.3 Predictionintervals 39
2.4 Modeltesting 42
2.5 Checkingnormality 43
2.6 Transformations 48
2.7 Inferenceaboutσ2 51
2.7.1 Theory 54
2.8 Exercises 55
3 GeneralStatisticalInference 57
3.1 Model-basedtesting 58
3.1.1 AnalternativeF test 64
3.2 Inferenceonsingleparameters:assumptions 64
3.3 Parametrictests 66
3.4 Confidenceintervals 70
3.5 Pvalues 72
3.6 Validityoftestsandconfidenceintervals 75
3.7 Theoryofpredictionintervals 75
ix