Accounting for multiple membership data in adolescent social networks : an analysis of simulated data

Multilevel modeling allows for the modeling of nested structures such as students nested within middle schools and middle schools nested within high schools. These kinds of hierarchies are common in social science research. Pure hierarchies may exist, where one variable is completely nested within another. Multiple membership (MM) structures occur when some lower level units are members of more than one higher level clustering unit (e.g., a student attends more than one high school). An extension to the conventional multilevel model, the multiple membership random effects model (MMREM) can be used to handle MM data. I compare a random effects model with and without multiple membership effects to demonstrate the possible benefit of accounting for the MM structure. We replicate an existing study on student academic outcomes (Tranmer et al., 2013) which assumes a multiple membership data structure, and add a comparison to a non-MM (i.e. single membership) model in order to assess the improvement in model fit. The original study investigated the effect of school, area, and social network membership in friendship dyads and triads on academic achievement in adolescents, with age, gender, and ethnicity as covariates. Our models retain the MM structure found in the original social network data. The original data is confidential and unavailable for use – therefore, a major component of this report is the simulation of this dataset in R. Results indicate that multiple membership does not necessarily lead to better goodness-of-fit as measured by DIC. Accounting for MM data structure initially produced a worse-fitting model. Artificially inflating the fixed and random effects that generated the simulated academic performance outcome led to the opposite effect. We conclude that the scale of random effects is important in determining the DIC measure of fit, and propose a full simulation study to more conclusively test our original hypothesis.