Tranmer, Mark; Steel, David; and Browne, William J., Multiple membership models for social network and group dependencies, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 1-12, 2012, 17.
Multilevel models have been developed and applied for individuals in groups, such as schools or areas, but these models tend to not consider the networks of an individual’s connections within and between groups; the social network has largely been ignored as an additional source of dependence in multilevel modelling that is carried out in social statistics. Typical models for network dependencies in the social networks literature, such as network autocorrelation models, have largely ignored other sources of dependence, such as the school or area in which an individual lives. To bridge this divide, a multiple membership modelling approach for jointly investigating social network and group dependencies is presented that allows social network and group dependencies on individual responses to be investigated and compared, and which can be analysed using MCMC estimation in standard statistical software for multilevel modelling. This approach is used to analyse a subsample of the Adolescent Health dataset from the US, where the two response variables of interest are individual level educational attainment and self-assessed health status, and the three individual level covariates are sex, ethnic group and age. Individual, network, school and area levels are included in the analysis. The network level can be represented with various configurations. The results suggest that the network should not be ignored from a statistical perspective when studying variations in educational attainment, as ignoring this level impacts on the estimates of variation at the other levels (school, area, individual), as well as having some impact on the point estimates and standard errors of the estimates of regression coefficients for covariates in the fixed part of the model. From a substantive perspective, this approach provides a flexible and practical way of investigating the network level, and comparing its relative importance to other group levels such as areas or schools.