Point process modeling for directed interaction networks (1011.1703v3)

Abstract: Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors 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--those involving a single sender but multiple receivers--are treated explicitly. The resulting inferential framework is then employed to model message sending behavior in a corporate e-mail network. The analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection.

• The paper introduces a Cox proportional intensity model that incorporates static and dynamic covariates to predict interaction patterns.
• It robustly measures the impact of network traits and history on communication likelihood, validated with Enron email data.
• Its methodology offers significant practical insights for organizational and social network analysis, paving the way for future research.

An Expert Overview of "Point Process Modeling for Directed Interaction Networks"

The paper "Point Process Modeling for Directed Interaction Networks" by Patrick O. Perry and Patrick J. Wolfe provides a rigorous statistical framework for analyzing network data comprising repeated interactions between individuals. These interactions could be in the form of communications such as emails, text messages, or phone calls within a network. The primary objective of the paper is to ascertain which traits and behaviors are predictive of these interactions. To achieve this, the authors employ a Cox multiplicative intensity model to treat directed interactions as a multivariate point process.

Methodological Contribution

The authors propose a Cox proportional intensity model that incorporates both static and history-dependent covariates to analyze interaction data. The model is particularly adept at handling dynamic social interactions because it allows covariates to vary with time and depend on the past interactions, making it suitable for rich, time-stamped network data. The model's robustness is further enhanced by proving consistency and asymptotic normality of partial-likelihood-based estimators under specific regularity conditions.

An efficient fitting procedure is outlined, which is particularly crucial given the high dimensionality and temporal nature of network datasets. The authors address multicast interactions, where a single sender may communicate with multiple receivers simultaneously, which is an important consideration for practical applications like email communications.

Application and Results

To demonstrate the model's applicability, Perry and Wolfe analyze a corporate email network dataset from Enron, including over 21,000 messages sent within the company. They employ the model to quantify the effects of both static shared traits (e.g., department, gender, seniority) and dynamic network behaviors (e.g., prior interactions) on the likelihood of message exchanges. The analysis highlights several critical findings:

1. Homophily and Network Effects: The authors explore the extent to which shared characteristics and previous interactions impact future communications. For instance, they examine whether individuals are more likely to interact if they belong to the same department or have communicated frequently in the past.
2. Model Efficacy: The paper's model accounts for a significant portion of the observed variance in the network data, especially when incorporating dynamic network covariates. This indicates the model's strong predictive capability and its utility in understanding complex interaction dynamics.
3. Practical Implications: The ability to quantify interaction predictors holds practical significance for organizational communication analysis, social media interaction, and other fields reliant on understanding directed network flows.

Theoretical Implications and Future Directions

On the theoretical front, the paper extends existing survival analysis methodologies to the field of network data, offering a robust inferential framework for directed interactions. The paper also points out the limitations and biases introduced when treating multicast interactions with ad-hoc solutions like duplication, providing avenues for future methodological improvements.

Looking forward, these foundational results open opportunities for further research into dynamic network modeling. For instance, future work could investigate alternative covariate structures and models that incorporate more complex network dependencies. Additionally, the extension to larger and more diverse datasets could illustrate the model's scalability and generalizability across varying domains.

Overall, Perry and Wolfe's paper makes substantial contributions both in terms of methodology and application, providing researchers with a powerful tool for examining the intricate dynamics of directed interaction networks while setting the stage for subsequent research in the area of dynamic network modeling.