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Harry Khamis
Statistical Consulting Center Department of Mathematics and Statistics College of Science and Mathematics Wright State Home
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Graphical Models and Multigraph Representations 

Numbers in parentheses correspond to the numbered references in my publication list.

A very useful technique for analyzing and interpreting hierarchical loglinear models in a graphical way was introduced by Darroch, Lauritzen, and Speed (1980) in a landmark paper. The usefulness of this approach is principally due to the simple graphical characterization of models that can be understood purely in terms of conditional independence relationships. Beginning with this paper, chordal graphs have emerged as an important type of model for the statistical analysis of contingency tables. A limited survey of this literature is given in (50). 

An alternative approach to that of Darroch et al. makes use of the generator multigraph. The multigraph approach has several strategic advantages over the first-order interaction graph used by Darroch et al. An account of how to use the multigraph approach in maximum likelihood estimation and in identifying conditional independencies in hierarchical loglinear models, as well as examples, are given in (41). The theoretical details can be found in (43). 

One of the examples given in (41) involves data from the Dayton Area Drug Survey, a survey conducted in 1992 by the Wright State University School of Medicine and the United Health Services of the Dayton area (a United Way agency) of all Dayton area school children in grades 6 through 12. The Statistical Consulting Center at Wright State analyzed this very large, complex set of data. The multigraph approach was used to interpret structural relationships among the variables. It was gratifying to have the opportunity to use a statistical method developed by Wright State researchers (43) in analyzing data from a survey conducted cooperatively by Wright State and a Dayton United Way agency. Results of the study enhanced understanding and knowledge of drug and substance abuse by Dayton area youth.

In the SAGE monograph #167, a brief review of the loglinear model and a presentation of the association graph and the multigraph are given --- see (82). 



Darroch, J.N., Lauritzen, S.L., and Speed, T.P. (1980). Markov fields and loglinear interaction models for contingency tables. Annals of Statistics 8: 522-539.


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Prof. Harry Khamis, Director [e-mail]
Statistical Consulting Center [home][e-mail]
130 Mathematics and Microbiological Sciences Building
Wright State University
3640 Colonel Glenn Highway
Dayton OH 45435 USA
office phone: (937) 775-2433
or stat consulting center (937) 775-4205

fax: (937) 775-2081
Last updated: July 18, 2001
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