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Enumeration and Simulation Methods for 0–1 Matrices with Given Marginals

Published online by Cambridge University Press:  01 January 2025

Tom A. B. Snijders*
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen Department of Empirical Theoretical Sociology, University of Utrecht
*
Requests for reprints should be sent to Tom A. B. Snijders, VSM/FPPSW, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.

Abstract

Data in the form of zero-one matrices where conditioning on the marginals is relevant arise in diverse fields such as social networks and ecology; directed graphs constitute an important special case. An algorithm is given for the complete enumeration of the family of all zero-one matrices with given marginals and with a prespecified set of cells with structural zero entries. Complete enumeration is computationally feasible only for relatively small matrices. Therefore, a more useable Monte Carlo simulation method for the uniform distribution over this family is given, based on unequal probability sampling and ratio estimation. This method is applied to testing reciprocity of choices in social networks.

Type
Original Paper
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The author wishes to thank Cajo ter Braak and John Birks for pointing out the relevance of this subject for ecology; and also Albert Verbeek and Ivo Molenaar, a referee, the Editor, and the Associate Editor for their comments. An earlier version of this paper was presented at the Stockholm Conference on Random Graphs and Applications (April 25–27, 1989), organized with financial support from the Swedish Council of Research in the Humanities and the Social Sciences.

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