In this paper I present a new model of dyadic link formation for directed
networks that extends the classical model by Holland and Leinhardt 1981.
Agents are endowed with unobserved effects that govern their ability to establish
links (productivity) and to receive links (popularity). The unobserved
effects are modelled by a fixed effects approach allowing for arbitrary correlation
between the observed homophily component and latent sources of degree
heterogeneity. The model can be estimated by conditional ML but inference
is non-standard due to the incidental parameters problem (Neyman and Scott
1948). I consider estimation of the parametric part of the linking model as
well as estimation of a measure of network transitivity. Moreover, I suggest a
specification test for the dyadic model based on predicted transitivity. My
approach overcomes the incidental parameters problem by using explicit
correction formulas based on an asymptotic approximation that sends the
number of agents to infinity. My simulation design suggests promising finite
sample performance. A linking model neglecting unobserved sources of degree
heterogeneity predicts an insuficient amount of transitivity. This effect is
proven for a stylized model and its empirical relevance is confirmed using
data on favor networks in Indian villages. In this application, a transitivity
statistic changes sign when unobserved agent effects are added. This suggests
that, in the real world, unobserved heterogeneity may be a primary driver of
local clustering behavior.