Generalized linear mixed-model (GLMM) trees: A flexible decision-tree method for multilevel and longitudinal data

Objective: Decision-tree methods are machine-learning methods which provide results that are relatively easy to interpret and apply by human decision makers. The resulting decision trees show how baseline patient characteristics can be combined to predict treatment outcomes for individual patients, for example. This paper introduces GLMM trees, a decision-tree method for multilevel and longitudinal data. Method: To illustrate, we apply GLMM trees to a dataset of 3,256 young people (mean age 11.33, 48% girls) receiving treatment at one of several mental-health service providers in the UK. Two treatment outcomes (mental-health difficulties scores corrected for baseline) were regressed on 18 demographic, case and severity characteristics at baseline. We compared the performance of GLMM trees with that of traditional GLMMs and random forests. Results: GLMM trees yielded modest predictive accuracy, with cross-validated multiple R values of .18 and .25. Predictive accuracy did not differ significantly from that of traditional GLMMs and random forests, while GLMM trees required evaluation of a lower number of variables. Conclusion: GLMM trees provide a useful data-analytic tool for clinical prediction problems. The supplemental material provides a tutorial for replicating the GLMM tree analyses in R.