Introduction to Graphical Modelling
Graphical modelling is a form of multivariate analysis that uses graphs to represent models. Although its roots can be traced back to path analysis (Wright, 1921) and statistical physics (Gibbs, 1902), its modern form is of recent origin. Key papers in the modern development include Darroch, Lauritzen, and Speed (1980), and Lauritzen and Wermuth (1989).
The purpose of this book is to provide a concise, application-oriented introduction to graphical modelling. The theoretical coverage is informal, and should be supplemented by other sources: the book by Whittaker (1990) would be a natural choice. Readers primarily interested in discrete data should consult the introductory-level book by Christensen (1990). Lauritzen (1992) provides a mathematically rigorous treatment: this is the source to consult about results stated here without proof.
Applications of graphical modelling in a wide variety of areas are shown. These analyses make use of l’v1IM, a command-driven PC-program designed for graphical modelling. A student version of l’v1IM is included with the book, and a reference guide is included as an appendix.
My interest in graphical modelling started in 1978-1980 under the influence of Terry Speed, who held a seminal lecture course on the topic in Copenhagen in 1978. Subsequent participation in a study group on graphical modelling, together with Steffen Lauritzen, Svend Kreiner, Morten Frydenberg, Jens Henrik Badsberg, and Poul Svante Eriksen, has served to stimulate and broaden my interest in the topic.
The first version of MlM was written in 1986-1987 at the Statistical Research Unit, Copenhagen University, when I was supported by a Danish Social Science Research Council grant. I wish to thank all the people who helped in the development of l’v1IM, including: Brian Murphy, for assistance and inspiration, and for kindly supplying the program LOLITA which served as a starting point for MIl’v’I; Morten Frydenberg, for crucial assistance with the modified iterative proportional scaling (MIPS) algorithm; Steffen Lauritzen, Nanny Wermuth, Hanns-Georg Leimer, Svend Kreiner, Jens Henrik Badsberg, and Joe Whittaker for encouraging help; Brian Francis and Joe Whittaker for contributing the SUSPEND and RETURN commands; Egon Hansen for help with the interactive graphics; The Tjur for generously letting me use his module for distribution functions; Svend Kreiner for helping me code Patefield’s (1981) algorithm; and Marta Honikova for programming the explicit estimation and EH-selection procedures.
Finally, thanks are also due to Peter Smith, Philip Hougaard, and Helle Lynggaard for helpful suggestions.
January 28, 1995
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