Assessment of Multiple Membership Multilevel Models: An Application to Interviewer Effects on Nonresponse.

Multilevel multiple membership models account for situations where lower level units are nested within multiple higher level units from the same classification. Not accounting correctly for such multiple membership structures leads to biased results. The use of a multiple membership model requires selection of weights reflecting the hypothesized contribution of each level two unit and their relationship to the level one outcome. The Deviance Information Criterion (DIC) has been proposed to identify such weights. For the case of logistic regression, this study assesses, through simulation, the model identification rates of the DIC to detect the correct multiple membership weights, and the properties of model variance estimators for different weight specifications across a range of scenarios. The study is motivated by analyzing interviewer effects across waves in a longitudinal study. Interviewers can substantially influence the behavior of sample survey respondents, including their decision to participate in the survey. In the case of a longitudinal survey several interviewers may contact sample members to participate across different waves. Multilevel multiple membership models are suitable to account for the inclusion of higher-level random effects for interviewers at various waves, and to assess, for example, the relative importance of previous and current wave interviewers on current wave nonresponse. To illustrate the application, multiple membership models are applied to the UK Family and Children Survey to identify interviewer effects in a longitudinal study. The paper takes a critical view on the substantive interpretation of the model weights and provides practical guidance to statistical modelers. The main recommendation is that it is best to specify the weights in a multiple membership model by exploring different weight specifications based on the DIC, rather than prespecifying the weights.