Tree-based varying coefficient regression for longitudinal ordinal responses

A tree-based algorithm for longitudinal regression analysis that aims to learn whether and how the effects of predictor variables depend on moderating variables is presented. The algorithm is based on multivariate generalized linear mixed models and it builds piecewise constant coefficient functions. Moreover, it is scalable for many moderators of possibly mixed scales, integrates interactions between moderators and can handle nonlinearities. Although the scope of the algorithm is quite general, the focus is on its usage in an ordinal longitudinal regression setting. The potential of the algorithm is illustrated by using data derived from the British Household Panel Study, to show how the effect of unemployment on self-reported happiness varies across individual life circumstances.11R-codes and datasets are available online as supplementary files (see Appendix B).