Transformation Analysis in R


Lecturers Dr. Torsten Hothorn, UZH, Institut für Epidemiologie, Biostatistik und Prävention
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Novice and advanced R users from all professional groups.
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Regression models for supervised learning problems with a continuous response are commonly understood as models for the conditional mean of the response given predictors. This notion is simple and therefore appealing for interpretation and visualisation. Information about the whole underlying conditional distribution is, however, not available from these models. A more general understanding of regression models as models for conditional distributions allows much broader inference from such models, for example the computation of prediction intervals.

Transformation models describe conditional distributions in a simple yet powerful and extensible way. This class of models relies on a parametric family of distributions characterised by their transformation function. Well-known classics, such as the normal linear regression models, binary and polytomous logistic regression, or Weibull and Cox regression models can all be understood as special transformation models. The first part of this tutorial highlights the connections between these models in very simple terms. Furthermore, a general form of the likelihood allowing arbitrary forms of random censoring and truncation will be introduced. Finally, model estimation using the R add-on packages mlt and tram will be illustrated by regression models for binary, ordered, continuous, and potentially censored response variables.

Based on these relatively simple and well-known classical models, the second part of this tutorial introduces novel conditional transformation models. In particular, we will discuss procedures for distribution regression (that is, models with response-varying linear effects) as well as transformation trees and corresponding forests as locally adaptive maximum likelihood estimators. The resulting predictive distributions are fully parametric yet very general and allow inference procedures, such as likelihood-based variable importances, to be applied in a straightforward way. The procedure allows general transformation models to be estimated without the necessity of a priori specifying the dependency structure of parameters. Applications include the computation of probabilistic forecasts, modelling differential treatment effects, or the derivation of counterfactural distributions for all types of response variables. A range of potential applications will be illustratedby the corresponding implementation in the trtf R add-on package.

Links The mlt Package (JSS, forthcoming), Most Likely Transformations(SJoS, 2018), Conditional Transformation Models (JRSS-B, 2014), Transformation Forests (arXiv, 2017)

September 26-27, 2019


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