[Paper Review] Beyond Homophily: Incorporating Actor Variables in Actor-oriented Network Models

Tom A. B. Snijders, Alessandro Lomi|arXiv (Cornell University)|Mar 19, 2018

Complex Network Analysis Techniques43 references3 citations

TL;DR

This paper proposes a four-parameter quadratic model to simultaneously capture homophily, aspiration, attachment conformity, and sociability in directed networks using numerical actor attributes. Applied to an MBA advice network, the model reveals homophily and moderate aspiration effects, demonstrating that confounding mechanisms beyond homophily must be considered for accurate network modeling.

ABSTRACT

We consider the specification of effects of numerical actor attributes in statistical models for directed social networks. A fundamental mechanism is homophily or assortativity, where actors have a higher likelihood to be tied with others having similar values of the variable under study. But there are other mechanisms that may also play a role in how the attribute values of two actors influence the likelihood of a tie. We discuss three additional mechanisms: aspiration to send ties to others having high values; conformity in the sense of sending more ties to others whose values are close to what may be considered the `social norm'; and sociability, where those having higher values will tend to send more ties generally. These mechanisms may operate jointly, and then their effects will be confounded. We present a specification representing these effects simultaneously by a four-parameter quadratic function of the values of sender and receiver. Greater flexibility can be obtained by a five-parameter extension. We argue that empirical researchers often overlook the possibility that homophily may be confounded with these other mechanisms, and that for actor attributes that have important effects on directed networks, these specifications may provide an improvement. An illustration is given of the dependence of advice ties on academic grades in a network of MBA students, analyzed by the Stochastic Actor-oriented Model.

Motivation & Objective

• To address the limitation of focusing solely on homophily when modeling numerical actor attributes in directed networks.
• To identify and formalize four distinct mechanisms—homophily, aspiration, attachment conformity, and sociability—that influence tie formation.
• To develop a flexible, statistically grounded model that captures these mechanisms jointly, avoiding confounding effects.
• To demonstrate the empirical relevance of this model through an analysis of advice ties in an MBA cohort using academic grades as a numerical attribute.

Proposed method

• Proposes a four-parameter quadratic function of sender and receiver attribute values to model dyadic tie probabilities in directed networks.
• Extends the model to five parameters for greater flexibility, allowing separate estimation of homophily, aspiration, conformity, and sociability.
• Uses the Stochastic Actor-oriented Model (SAOM) to estimate the model on longitudinal network data.
• Implements the model in the RSiena software using dyadic covariates such as egoX, diffSqX, altX, altSqX, and egoXaltX.
• Applies the delta method to estimate standard errors for the derived social norm value, a nonlinear function of model parameters.
• Employs method-of-moments estimation with covariance matrix approximation for parameter inference.

Experimental results

Research questions

• RQ1 How do homophily, aspiration, attachment conformity, and sociability jointly influence tie formation in directed networks with numerical attributes?
• RQ2 To what extent is homophily confounded with other mechanisms when modeling numerical actor attributes in network data?
• RQ3 Can a quadratic model with four or five parameters better capture the true dependence of tie formation on actor attributes than simpler models?
• RQ4 What is the empirical relevance of these mechanisms in a real-world advice network among MBA students?
• RQ5 How can the social norm value, derived from model parameters, be estimated and its uncertainty quantified?

Key findings

• In the MBA advice network, homophily was strongly supported, indicating students were more likely to advise peers with similar academic grades.
• Aspiration, defined as a tendency to advise higher-achieving peers, showed a medium-strength effect, though not statistically significant.
• No significant evidence was found for attachment conformity, where actors would prefer peers close to a social norm.
• Sociability, or general tendency to form more ties with higher-attribute values, was not associated with academic grades in this dataset.
• The four-parameter quadratic model provided a better fit than simpler models by disentangling confounded mechanisms.
• The five-parameter extension offered increased flexibility, though the four-parameter version was sufficient for the empirical data.