Multidimensional homophily

Homophily is typically measured using a single dimension to define groups. However, people generally display friendship preferences over multiple dimensions when forming social connections. We develop a simple model that characterizes agents both by a (discrete) “group type” and a (continuous) “personality trait” value. Agents have preferences-for-similarity over both dimensions, but homophily is only measured with respect to group type. We show that our model belongs to a more general class of models for which a strongly stable network exits, and identify an algorithm that constructs it. Via simulations, we demonstrate that our model's strongly stable network exhibits three key patterns previously documented in the homophily literature. The model provides new insights and interpretations of these patterns.