Edwards, D. (2000), Introduction to Graphical Modelling, 2nd ed., Springer-Verlag, New York.

Graphical modelling is a form of multivariate analysis that uses graphs to represent models. These graphs display the structure of dependencies, both associational and causal, between the variables in the model. This textbook provides an introduction to graphical models with emphasis on applications and practicalities rather than a formal development. It is based on the popular software package for graphical modelling, MIM, a freeware version of which can be downloaded from the internet.

Following an introductory chapter which sets the scene and describes some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models with mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to the second edition. Chapter 7 describes the use of directed graphs, chain graphs, and other graphs. Chapter 8 summarizes some recent work on causal inference, relevant when graphical models are given a causal interpretation.

This book will provide a useful introduction to this topic for students and researchers.

Table of contents:

  1. Preliminaries
    1. Independence and Conditional Independence
    2. Undirected Graphs
    3. Data, Models and Graphs
    4. Simpson's Paradox
    5. Overview of the Book
  2. Discrete Models
    1. Three-way Tables
    2. Multi-way Tables
  3. Continuous Models
    1. Graphical Gaussian Models
    2. Regression Models
  4. Mixed Models
    1. Hierarchical Interaction Models
    2. Breaking Models into Smaller Ones
    3. Mean Linearity
    4. Decomposable Models
    5. CG-Regression Models
    6. Incomplete Data
    7. Discriminant Analysis
  5. Hypothesis Testing
    1. An Overview
    2. Chi-square Tests
    3. F-tests
    4. Exact Conditional Tests
    5. Deviance-Based Tests
    6. Permutation F-test
    7. Pearson Chi-squared Test
    8. Fisher's Exact Test
    9. Rank Tests
    10. Wilcoxon Test
    11. Kruskal-Wallis Test
    12. Jonckheere-Terpstra Test
    13. Tests for Variance Homogeneity
    14. Tests for Equality of Means Given Homogeneity
    15. Hotellings T2
  6. Model Selection and Criticism
    1. Stepwise Selection
    2. The EH-Procedure
    3. Selection Using Information Criteria
    4. Comparison of the Methods
    5. Box-Cox Transformations
    6. Residual Analysis
    7. Dichotomization
  7. Directed Graphs and Their Models
    1. Directed Acyclic Graphs
    2. Chain Graphs
    3. Local Independence Graphs
    4. Covariance Graphs
    5. Chain Graphs with Alternative Markov Properties
    6. Reciprocal Graphs
  8. Causal Inference
    1. Philosophical Aspects
    2. Rubin's Causal Model
    3. Pearl's Causal Graphs
    4. Discussion

 

  1. The MIM Command Language
  2. Implementation Specifics of MIM
  3. On Multivariate Symmetry
  4. On the Estimation Algorithms

 

References

Index

2000, 333 pp. Hardcover ISBN 0-387-95054-0.