Network autocorrelation models with egocentric data

- Network autocorrelation models are adapted for egocentric network data.
- Models for actor attributes are derived from network effects and disturbances models.
- Correlation structures are compatible with models for the fully observed network.
- Proposed methods are feasible even if the network boundary is unknown or ill-defined.

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.