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
- Reorganized to focus on unbalanced data
- Reworked balanced analyses using methods for unbalanced data
- Introductions to nonparametric and lasso regression
- Introductions to general additive and generalized additive models
- Examination of homologous factors
- Unbalanced split plot analyses
- Extensions to generalized linear models
- R, Minitab®, and SAS code on the author’s website
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.
Table of Contents:
Introduction
Probability
Random variables and expectations
Continuous distributions
The binomial distribution
The multinomial distribution
One Sample
Example and introduction
Parametric inference about μ
Prediction intervals
Model testing
Checking normality
Transformations
Inference about σ2
General Statistical Inference
Model-based testing
Inference on single parameters: assumptions
Parametric tests
Confidence intervals
P values
Validity of tests and confidence intervals
Theory of prediction intervals
Sample size determination and power
The shape of things to come
Two Samples
Two correlated samples: Paired comparisons
Two independent samples with equal variances
Two independent samples with unequal variances
Testing equality of the variances
Contingency Tables
One binomial sample
Two independent binomial samples
One multinomial sample
Two independent multinomial samples
Several independent multinomial samples
Lancaster–Irwin partitioning
Simple Linear Regression
An example
The simple linear regression model
The analysis of variance table
Model-based inference
Parametric inferential procedures
An alternative model
Correlation
Two-sample problems
A multiple regression
Estimation formulae for simple linear regression
Model Checking
Recognizing randomness: Simulated data with zero correlation
Checking assumptions: Residual analysis
Transformations
Lack of Fit and Nonparametric Regression
Polynomial regression
Polynomial regression and leverages
Other basis functions
Partitioning methods
Splines
Fisher’s lack-of-fit test
Multiple Regression: Introduction
Example of inferential procedures
Regression surfaces and prediction
Comparing regression models
Sequential fitting
Reduced models and prediction
Partial correlation coefficients and added variable plots
Collinearity
More on model testing
Additive effects and interaction
Generalized additive models
Final comment
Diagnostics and Variable Selection
Diagnostics
Best subset model selection
Stepwise model selection
Model selection and case deletion
Lasso regression
Multiple Regression: Matrix Formulation
Random vectors
Matrix formulation of regression models
Least squares estimation of regression parameters
Inferential procedures
Residuals, standardized residuals, and leverage
Principal components regression
One-Way ANOVA
Example
Theory
Regression analysis of ANOVA data
Modeling contrasts
Polynomial regression and one-way ANOVA
Weighted least squares
Multiple Comparison Methods
"Fisher’s" least significant difference method
Bonferroni adjustments
Scheffé’s method
Studentized range methods
Summary of multiple comparison procedures
Two-Way ANOVA
Unbalanced two-way analysis of variance
Modeling contrasts
Regression modeling
Homologous factors
ACOVA and Interactions
One covariate example
Regression modeling
ACOVA and two-way ANOVA
Near replicate lack-of-fit tests
Multifactor Structures
Unbalanced three-factor analysis of variance
Balanced three-factors
Higher-order structures
Basic Experimental Designs
Experiments and causation
Technical design considerations
Completely randomized designs
Randomized complete block designs
Latin square designs
Balanced incomplete block designs
Youden squares
Analysis of covariance in designed experiments
Discussion of experimental design
Factorial Treatments
Factorial treatment structures
Analysis
Modeling factorials
Interaction in a Latin square
A balanced incomplete block design
Extensions of Latin squares
Dependent Data
The analysis of split-plot designs
A four-factor example
Multivariate analysis of variance
Random effects models
Logistic Regression: Predicting Counts
Models for binomial data
Simple linear logistic regression
Model testing
Fitting logistic models
Binary data
Multiple logistic regression
ANOVA type logit models
Ordered categories
Log-Linear Models: Describing Count Data
Models for two-factor tables
Models for three-factor tables
Estimation and odds ratios
Higher-dimensional tables
Ordered categories
Offsets
Relation to logistic models
Multinomial responses
Logistic discrimination and allocation
Exponential and Gamma Regression: Time-to-Event Data
Exponential regression
Gamma regression
Nonlinear Regression
Introduction and examples
Estimation
Statistical inference
Linearizable models
Appendix A: Matrices and Vectors
Appendix B: Tables
Exercises appear at the end of each chapter.
About the Author :
Ronald Christensen is a professor of statistics in the Department of Mathematics and Statistics at the University of New Mexico. Dr. Christensen is a fellow of the American Statistical Association (ASA) and Institute of Mathematical Statistics. He is a past editor of The American Statistician and a past chair of the ASA’s Section on Bayesian Statistical Science. His research interests include linear models, Bayesian inference, log-linear and logistic models, and statistical methods.
Review :
Praise for the First Edition:
"… written in a clear and lucid style … an excellent candidate for a beginning level graduate textbook on statistical methods … a useful reference for practitioners."
—Zentralblatt für Mathematik
"Being devoted to students mainly, each chapter includes illustrative examples and exercises. The most important thing about this book is that it provides traditional tools for future approaches in the big data domain since, as the author says, the machine learning techniques are directly based on the fundamental statistical methods."
~Marina Gorunescu (Craiova)
