The Effects of Omitting Components in a Multilevel Model With Social Network Effects

Abstract

Multilevel models are often used to account for the hierarchical structure of social data and the inherent dependencies to produce estimates of regression coefficients, variance components associated with each level, and accurate standard errors. Social network analysis is another important approach to analysing complex data that incoproate the social relationships between a number of individuals. Extended linear regression models, such as network autoregressive models, have been proposed that include the social network information to account for the dependencies between persons. In this article, we propose three types of models that account for both the multilevel structure and the social network structure together, leading to network autoregressive multilevel models. We investigate theoretically and empirically, using simulated data and a data set from the Dutch Social Behavior study, the effect of omitting the levels and the social network on the estimates of the regression coefficients, variance components, network autocorrelation parameter, and standard errors.