Finding structure in data using multivariate tree boosting
This work addresses the problem of interpreting complex multivariate data in psychology and psychiatry, offering a practical tool for researchers, though it is incremental as it builds on existing boosting techniques.
The authors tackled the challenge of finding structure in large psychological datasets with multiple outcomes by introducing multivariate tree boosting, a method that extends gradient boosted regression trees to handle multivariate outcomes, and demonstrated its effectiveness in identifying important predictors and achieving high prediction accuracy, often exceeding or matching existing methods.
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.