  Technology and collaboration enable dramatic increases in the size of
psychological and psychiatric data collections, but finding structure in these
large data sets with many collected variables is challenging. Decision tree
ensembles like random forests (Strobl, Malley, and Tutz, 2009) are a useful
tool for finding structure, but are difficult to interpret with multiple
outcome variables which are often of interest in psychology. To find and
interpret structure in data sets with multiple outcomes and many predictors
(possibly exceeding the sample size), we introduce a multivariate extension to
a decision tree ensemble method called Gradient Boosted Regression Trees
(Friedman, 2001). Our method, multivariate tree boosting, can be used for
identifying important predictors, detecting predictors with non-linear effects
and interactions without specification of such effects, and for identifying
predictors that cause two or more outcome variables to covary without
parametric assumptions. We provide the R package 'mvtboost' to estimate, tune,
and interpret the resulting model, which extends the implementation of
univariate boosting in the R package 'gbm' (Ridgeway, 2013) to continuous,
multivariate outcomes. To illustrate the approach, we analyze predictors of
psychological well-being (Ryff and Keyes, 1995). Simulations verify that our
approach identifies predictors with non-linear effects and achieves high
prediction accuracy, exceeding or matching the performance of (penalized)
multivariate multiple regression and multivariate decision trees over a wide
range of conditions.
