  In medical, social, and behavioral research we often encounter datasets with
a multilevel structure and multiple correlated dependent variables. These data
are frequently collected from a study population that distinguishes several
subpopulations with different (i.e., heterogeneous) effects of an intervention.
Despite the frequent occurrence of such data, methods to analyze them are less
common and researchers often resort to either ignoring the multilevel and/or
heterogeneous structure, analyzing only a single dependent variable, or a
combination of these. These analysis strategies are suboptimal: Ignoring
multilevel structures inflates Type I error rates, while neglecting the
multivariate or heterogeneous structure masks detailed insights. To analyze
such data comprehensively, the current paper presents a novel Bayesian
multilevel multivariate logistic regression model. The clustered structure of
multilevel data is taken into account, such that posterior inferences can be
made with accurate error rates. Further, the model shares information between
different subpopulations in the estimation of average and conditional average
multivariate treatment effects. To facilitate interpretation, multivariate
logistic regression parameters are transformed to posterior success
probabilities and differences between them. A numerical evaluation compared our
framework to less comprehensive alternatives and highlighted the need to model
the multilevel structure: Treatment comparisons based on the multilevel model
had targeted Type I error rates, while single-level alternatives resulted in
inflated Type I errors. Further, the multilevel model was more powerful than a
single-level model when the number of clusters was higher. ...
