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A primary question to ask of such data is which traits and behaviours are predictive of interaction. To answer this question, a model is introduced for treating directed interactions as a multivariate point process: a Cox multiplicative intensity model using covariates that depend on the history of the process. Consistency and asymptotic normality are proved for the resulting partial-likelihood-based estimators under suitable regularity conditions, and an efficient fitting procedure is described. Multicast interactions\u2014those involving a single sender but multiple receivers\u2014are treated explicitly. The resulting inferential framework is then employed to model message sending behaviour in a corporate e-mail network. 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