Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis

Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences.This two-volume work is a comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. Volume 1 examines models with balanced data (orthogonal models); Volume 2 studies models with unbalanced data (nonorthogonal models).Accessible to readers with only a modest mathematical and statistical background, the work will appeal to a broad audience of students, researchers, and practitioners in the mathematical, life, social, and engineering sciences. It may be used as a textbook in upper-level undergraduate and graduate courses, or as a reference for readers interested in the use of random effects models for data analysis.

Table of Contents:
Matrix Preliminaries and General Linear Model.- Some General Methods for Making Inferences about Variance Components.- One-Way Classification.- Two-Way Crossed Classification without Interaction.- Two-Way Crossed Classification with Interaction.- Three-Way and Higher-Order Crossed Classifications.- Two-Way Nested Classification.- Three-Way Nested Classification.- General r-Way Nested Classification.

Review :
From the reviews: "This is the second of a two-volume comprehensive review of the analysis of variance for random effects models.  Volume I was devoted to various models using balanced data, whereas this volume is concerned with unbalanced data.  The book provides extensive coverage of the methods and techniques of point estimation, interval estimation and tests of hypotheses for random effects models.  A variety of experimental designs are considered involving one, two, three and multi-factor experiments with crossed and nested factors.  Throughout the text, the procedures are illustrated using numerical examples analyzed with several software systems.... The book will be particularly useful as a reference source to the literature of random effects models with each chapter having its own bibliography and with the main extensive reference section containing more than six hundred papers." —Short Book Reviews of the International Statistical Institute "The book presents the theory, methods, data analysis, and applications requiring measurements of variance from several fields as agriculture, biology, applied genetics, animal breeding, medicine as well as eco-social sciences, including econometrics, quality control, and engineering. Numerical examples are given to analyse data and illustrate the theory and methods.… This monograph is an excellent book giving a survey of major theoretical and methodological developments for scientific research and application-oriented scientists." —Zentralblatt Math Review of both volumes "This two-volume set provides an encyclopedic and historical account of the theory and application of classical random-effects models.… For users of random-effects models and those interested in the theoretical development of this topic, these books are a valuable resource.… Throuhgout the [text], the authors go to great lengthsto provide references to original sources that would allow the reader to fill in details that are not included in the text.… By selecting an appropriate subset of topics, an instructor could create an outstanding graduate-level course on random-effects models.… These books provide an excellent unified reference on the methodological developments associated with classical random-effects models over the past 50 years." —Journal of the American Statistical Association "This is the second volume of a two-volume monograph on analysis of variance for random and mixed linear models. … This book presents a systematic and comprehensive coverage of different methods and techniques, mainly of point estimations … . At the end of each chapter there is a wide variety of well-chosen exercises … . Each chapter ends with a complete bibliography for the references in that chapter. The book … is well written." (Jon Stene, Mathematical Reviews, Issue 2006 i)