Multilevel Models for Multilevel Network Dependencies

Abstract

We explain how a type of multilevel model called a Multiple Membership Multiple Classification (MMMC) model can be used to investigate multilevel network dependencies for a nodal dependent variable at the lowest level of such a structure. In particular, the MMMC model allows us to estimate the relative share of variation in the dependent variable across the various components of a multilevel network in which it is embedded. We illustrate the approach with a case study: an analysis of the French cancer elites multilevel network data, collected by Lazega et al. (Soc Netw 30(2):159–176, 2008), which includes ties between individual researchers (the level 1 network), and ties between the laboratories in which they work (the level 2 network), as well as the affiliations of researchers (level 1 nodes) to laboratories (level 2 nodes). Our dependent variable in the case study is an interval-scale performance score for each researcher, which is a level 1 network nodal variable. We first fit null models to estimate the extent of variation in the dependent variable across the multilevel network, and later add explanatory variables to the fixed part of the model to investigate their association with research performance, and also to determine whether they explain any of the variation in research performance across the multilevel network. We find that network variation in the performance of the researchers is particularly associated with the way in which researchers nominate other researchers (their outgoing ties), and that some characteristics of the researchers are associated with differences in research performance, in particular the speciality of the researcher. We draw conclusions about the research value of the MMMC for multilevel networks and briefly discuss further extensions to the model.