Components of Variance
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Summary
Identifying the sources and measuring the impact of haphazard variations are important in any number of research applications, from clinical trials and genetics to industrial design and psychometric testing. Only in very simple situations can such variations be represented effectively by independent, identically distributed random variables or by random sampling from a hypothetical infinite population.
Components of Variance illuminates the complexities of the subject, setting forth its principles with focus on both the development of models for detailed analyses and the statistical techniques themselves. The authors first consider balanced and unbalanced situations, then move to the treatment of non-normal data, beginning with the Poisson and binomial models and followed by extensions to survival data and more general situations. In the final chapter, they discuss ways of extending and assessing various models, including the study of exceedances, the use of nonlinear representations, the study of transformations of the response variable, and the detailed examination of the distributional form of the underlying random variables.
Careful signposting and numerous examples from genetic data analysis, clinical trial design, longitudinal data analysis, industrial design, and meta-analysis make this book accessible - and valuable - not only to statisticians but to all applied research scientists who use statistical methods.
Table of Contents
KEY MODELS AND CONCEPTS
Preliminaries
Some Simple Special Models
A Distributional Specification
Two Key Concepts
Objectives
Bibliographic Notes
Further Results and Exercises
ONE-WAY BALANCED CASE
Analysis of Variance
Some More Assumptions
Synthesis of Variance
Finite Population Aspects
Formulation
Some More Theory
Bibliographic Notes
Computational/Software Notes
Further Results and Exercises
MORE GENERAL BALANCED ARRANGEMENTS
Preliminaries
Components of Covariance and Regression
Time as a Factor
Bayesian Considerations
Measurement Error in Regression
Heterogeneous Variability
Design Issues
Bibliographic Notes
Computational/Software Notes
Further Results and Exercises
UNBALANCED SITUATIONS
Introduction
One-Way Classification
A More General Formulation
A Special Case
Synthesis of Studies
Maximum Likelihood and REML
A Different Approach
Bibliographic Notes
Computational/Software Notes
Further Results and Exercises
NON-NORMAL PROBLEMS
Preliminaries
Poisson Distribution
Binomial Distribution
Survival Data
Some Extensions
A More General Formulation
Generalized Linear Mixed Model
Development of Analysis
An Outline Example
Bibliographic Notes
Computational/Software Notes
Further Results and Exercises
MODEL EXTENSIONS AND CRITICISM
Introduction
Modifications of Structure
Outliers
Robust Estimation of an Internal Variance
Model Assessment: Predicting Exceedances
Analysis of Variability Within Small Groups
Analysis by Model Elaboration: A Nonlinear Form
Analysis by Model Elaboration: Transformation
Nonparametric Estimation of Distributional Form
Bibliographic Notes
Further Results and Exercises
APPENDIX: Fitting Separate Logistic Regressions to the ANZICS Data
REFERENCES
AUTHOR INDEX
SUBJECT INDEX
Editorial Reviews
"The book succeeds in providing a good starting point for a statistician interested in an introduction to many of the issues associated with variance component estimation. … [V]ery approachable to a statistician with little background in the analysis of mixed models."
- Journal of the Americal Statistical Association, Sept. 2004, Vol. 99, No. 467
"Components of Variance is easy to read and to find examples. Its main features are the excellent discussions of the various models and the wealth of examples."
-Technometrics, 2003
"This is a superb book on a topic of central importance in a wide variety of areas of research. A particular strength is attention given to first principles as a prelude to the treatment of many of the technical topics. .... What distinguishes this book from other material is the depth of the discussion combined with the use of only essential technical details."
-Vern Farewell, MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK
"This is an excellent monograph that explores a variety of methods for understanding error variance."
-Journal of Mathematical Psychology, Vol. 49, 2005
