  Network autocorrelation models have been widely used for decades to model the
joint distribution of the attributes of a network's actors. This class of
models can estimate both the effect of individual characteristics as well as
the network effect, or social influence, on some actor attribute of interest.
Collecting data on the entire network, however, is very often infeasible or
impossible if the network boundary is unknown or difficult to define. Obtaining
egocentric network data overcomes these obstacles, but as of yet there has been
no clear way to model this type of data and still appropriately capture the
network effect on the actor attributes in a way that is compatible with a joint
distribution on the full network data. This paper adapts the class of network
autocorrelation models to handle egocentric data. The proposed methods thus
incorporate the complex dependence structure of the data induced by the network
rather than simply using ad hoc measures of the egos' networks to model the
mean structure, and can estimate the network effect on the actor attribute of
interest. The vast quantities of unknown information about the network can be
succinctly represented in such a way that only depends on the number of alters
in the egocentric network data and not on the total number of actors in the
network. Estimation is done within a Bayesian framework. A simulation study is
performed to evaluate the estimation performance, and an egocentric data set is
analyzed where the aim is to determine if there is a network effect on
environmental mastery, an important aspect of psychological well-being.
