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Title: Distribution-free location-scale regression Authors:  Sandra Siegfried - University of Zurich (Switzerland) [presenting]
Lucas Kook - University of Zurich, Zurich University of Applied Sciences (Switzerland)
Torsten Hothorn - University of Zurich (Switzerland)
Abstract: A generalized additive model for location, scale, and shape (GAMLSS) next of kin is introduced, aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution formulating such a model with a transformation function, which in turn is estimated from data. Doing so not only makes the model distribution-free but also allows limiting the number of linear or smooth model terms to a pair of location-scale predictor functions. The likelihood for continuous, discrete, and randomly censored observations, along with corresponding score functions, can be derived for these models. A plethora of existing algorithms is leveraged for model estimation, including constraint maximum-likelihood, the original GAMLSS algorithm, and transformation trees. Parameter interpretability in the resulting models is closely connected to model selection. We propose the application of a novel best subset selection procedure to achieve especially simple ways of interpretation. All techniques are motivated and illustrated by a collection of applications from different domains, including crossing and partial proportional hazards, complex count regression, nonlinear ordinal regression, growth curves, and receiver operating characteristics. The models can be estimated using the "tram" add-on package to the R system for statistical computing and graphics.