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Is there a statistical model that can study determinants of network linkage formation? For a set of companies (where we observe their industry, annual revenue, etc), we see which pairs are connected by buying-selling relationships, and we would like to see what characteristics of the companies are predictive of network links forming. A simple example would be for Buyer X in industry A, is the company more likely to buy from Sellers in the same industry. One way I've thought of is to use a probit regression to see for each characteristic of the sellers (e.g. industry), whether Buyer characteristics predict relationship formation (0/1 for whether relationship is formed), but are there better ways to do this?

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Graham (2017) (free version here) describes a model of link formation in networks that allows for homophily and unobservable node heterogeneity. His model might be applicable to your problem.

A simpler approach would be to estimate a probit/logit model as you suggested. However, you would need to adjust your estimates' standard errors to correct for the fact that your observations of dyads with common nodes are not independent. (For example, mean sales by companies A and B and not independent of mean sales by companies B and C.) Fafchamps and Gubert (2007) (free version here) demonstrate how to perform this correction using OLS.

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