The multivariate multiple-membership random-effect model: An introduction and evaluation.

In the present study, we focused on models that handle several data structure complexities simultaneously. We introduced and evaluated the multivariate multiple-membership random-effect model (MV-MMREM) for handling multiple-membership data in scenarios with multiple, related outcomes. Although a recent study introduced the idea of the MV-MMREM, no research has directly assessed its estimation nor demonstrated its use with real data. Therefore, we used real multiple-membership datasets that included multiple, related outcomes to demonstrate interpretation of the MV-MMREM parameters. In addition, a simulation study was conducted to assess estimation of the MV-MMREM under a number of design conditions. Also, the robustness of the results was assessed for multivariate multiple-membership data when they were analyzed using a multivariate hierarchical linear model that ignores the multiple-membership structure (MV-HLM), as well as when using multiple univariate MMREMs. The results showed that the MV-MMREM works well in comparison with both MV-HLM and univariate MMREMs when the data structure had missingness outcomes, multivariate outcomes, and multiple membership clusters. Finally, we discuss limitations of the MV-MMREM and areas for future research.