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Logit Models and Logistic Regressions for Social Networks: III. Valued Relations

Published online by Cambridge University Press:  01 January 2025

Garry Robins ,
Philippa Pattison  and
Stanley Wasserman
Garry Robins*
Affiliation:
Deakin University
Philippa Pattison
Affiliation:
University of Melbourne
Stanley Wasserman
Affiliation:
University of Illinois
*
Requests for reprints should be sent to Garry Robins, Faculty of Health and Behavioural Sciences, School of Psychology, Deakin University, Geelong Victoria 3217, AUSTRALIA.
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Abstract

This paper generalizes the p* model for dichotomous social network data (Wasserman & Pattison, 1996) to the polytomous case. The generalization is achieved by transforming valued social networks into three-way binary arrays. This data transformation requires a modification of the Hammersley-Clifford theorem that underpins the p* class of models. We demonstrate that, provided that certain (non-observed) data patterns are excluded from consideration, a suitable version of the theorem can be developed. We also show that the approach amounts to a model for multiple logits derived from a pseudo-likelihood function. Estimation within this model is analogous to the separate fitting of multinomial baseline logits, except that the Hammersley-Clifford theorem requires the equating of certain parameters across logits. The paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples.

Keywords

social networksp* modelsautologistic modelspseudo-likelihood estimation
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 3 , September 1999 , pp. 371 - 394
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

This research was supported by grants from the Australian Research Council, the National Science Foundation (#SBR96-30754), and the National Institute of Health (#PHS-1RO1-39829-01).

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