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. One Sample. General Statistical Inference. Two Samples. Contingency Tables. Simple Linear Regression. Model Checking. Lack of Fit and Nonparametric Regression. Multiple Regression: Introduction. Diagnostics and Variable Selection. Multiple Regression: Matrix Formulation. One-Way ANOVA. Multiple Comparison Methods. Two-Way ANOVA. ACOVA and Interactions. Multifactor Structures. Basic Experimental Designs. Factorial Treatments. Dependent Data. Logistic Regression: Predicting Counts. Log-Linear Models: Describing Count Data. Exponential and Gamma Regression: Time-to-Event Data. Nonlinear Regression. Appendices.
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.
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)