Abstract
This paper generalizes thep* 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 thep* 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.
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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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Robins, G., Pattison, P. & Wasserman, S. Logit models and logistic regressions for social networks: III. Valued relations. Psychometrika 64, 371–394 (1999). https://doi.org/10.1007/BF02294302
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DOI: https://doi.org/10.1007/BF02294302