The current dissertation, composed of two studies, focused on the models that handle several data structure complexities simultaneously. The first study introduced and evaluated Markov Chain Monte Carlo (MCMC) estimation of the multivariate multiple-membership random effects model (MV-MMREM) for handling multiple-membership data in scenarios with multiple, related outcomes. The second study assessed performance of the deviance information criterion (DIC) for selecting the best-fitting model to help support a researcher’s choices about whether to add fixed effects to the MV-MMREM effects model. While 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, real multiple-membership dataset were used that includes multiple related outcomes to demonstrate interpretation of MV-MMREM parameters. In addition, a simulation study was conducted to assess estimation of the MV-MMREM under a number of design conditions including the proportion of multiple membership individuals, the number of clusters, the sample size per cluster, the degree of correlation among pairs of outcomes, the true intra-class correlation coefficient, type of missingness, and proportion of missingness. Additionally, the robustness of results were assessed for multivariate multiple-membership data when analyzed using multivariate, hierarchical linear model that ignores the multiple-membership structure (MV-HLM) and when instead using multiple, univariate MMREMs (one for each outcome). The results were assessed using relative parameter bias (RPB), relative standard error bias (RSEB), and coverage rates. In the second study, another real dataset were analyzed with the resulting DIC values compared to demonstrate how it is used to support selection of the best-fitting model. In the associated simulation study, the same set of design conditions as in the first study (but not considered missingness and considered the magnitude of coefficients of predictor variables) were manipulated. The DIC was used to choose between three different conditional MV-MMREMs that differ in their fixed effects parameter specification. We assessed and compared correct model identification rates based on the DIC with inferences and based on the statistical significance of the parameters being added in the set of nested models.