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Journal of the American Statistical Association Volume 76, 1981 - Issue 373
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Invited Paper

An Exponential Family of Probability Distributions for Directed Graphs

Paul W. Holland Program Statistics Research, Educational Testing Service, Princeton, NJ, 08541, USA
&
Samuel Leinhardt School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, PA, 15213, USA
Pages 33-50 | Received 01 Apr 1979, Published online: 12 Mar 2012
 
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Abstract

Directed graph (or digraph) data arise in many fields, especially in contemporary research on structures of social relationships. We describe an exponential family of distributions that can be used for analyzing such data. A substantive rationale for the general model is presented, and several special cases are discussed along with some possible substantive interpretations. A computational algorithm based on iterative scaling procedures for use in fitting data is described, as are the results of a pilot simulation study. An example using previously reported empirical data is worked out in detail. An extension to multiple relationship data is discussed briefly.

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