Robust gradient boosting for generalized additive models for location, scale and shape

Due to the increasing complexity and dimensionality of data sources, it is favorable that methodological approaches yield robust results so that corrupted observations do not jeopardize overall conclusions. We propose a modelling approach which is robust towards outliers in the response variable for generalized additive models for location, scale and shape (GAMLSS). We extend a recently proposed robustification of the log-likelihood to gradient boosting for GAMLSS, which is based on trimming low log-likelihood values via a log-logistic function to a boundary depending on a robustness constant. We recommend a data-driven choice for the involved robustness constant based on a quantile of the unconditioned response variable and investigate the choice in a simulation study for low- and high-dimensional data situations. The versatile application possibilities of robust gradient boosting for GAMLSS are illustrated via three biomedical examples-including the modelling of thyroid hormone levels, spatial effects for functional magnetic resonance brain imaging and a high-dimensional application with gene expression levels for cancer cell lines.