  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.
