An empirical model of dyadic link formation in a network with unobserved heterogeneity

Abstract

In this paper I study a fixed effects model of dyadic link formation for directed networks. I discuss inference on structural parameters as well as a test of model specification. In the model, an agent's linking decisions depend on perceived similarity to potential linking partners(homophily). Agents are endowed with potentially unobserved characteristics that govern their ability to establish links (productivity) and to receive links (popularity). Heterogeneity in productivity and popularity is a structural driver of degree heterogeneity. The unobserved heterogeneity is captured by a fixed effects approach. This allows for arbitrary correlation between an observed homophily component and latent sources of degree heterogeneity.The linking model accounts for link reciprocity by allowing linking decisions within each pair of agents to be correlated. Estimates of structural parameters related to homophily preferences and reciprocity can be obtained by ML but inference is non-standard due to the incidental parameter problem (Neyman and Scott 1948). I study t-statistics constructed from ML estimates via a naive plug-in approach. For these statistics it is not appropriate to compute critical values from a standard normal distribution because of the incidental parameter problem. I suggest modified t-statistics that are justified by an asymptotic approximation that sends the number of agents to infinity. For a t-test based on the modified statistics, critical values can be computed from a standard normal distribution. My model specification test compares observed transitivity to the transitivity predicted by the dyadic linking model. The test statistic corrects for incidental parameter bias that is due to ML estimation of the null model. The implementation of my procedures is illustrated by an application to favor networks in Indianvillages.