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Distribution-Free Location-Scale Regression

Siegfried, Sandra; Kook, Lucas; Hothorn, Torsten (2023). Distribution-Free Location-Scale Regression. The American Statistician, 77(4):345-356.

Abstract

We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modeling for arbitrary outcomes. We replace the strict parametric distribution formulating such a model by a transformation function, which in turn is estimated from data. Doing so not only makes the model distribution-free but also allows to limit the number of linear or smooth model terms to a pair of location-scale predictor functions. We derive the likelihood for continuous, discrete, and randomly censored observations, along with corresponding score functions. A plethora of existing algorithms is leveraged for model estimation, including constrained 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, and growth curves. All analyses are reproducible with the help of the tram add-on package to the R system for statistical computing and graphics.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > General Mathematics
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, General Mathematics, Statistics and Probability
Language:English
Date:2 October 2023
Deposited On:15 Jan 2024 16:59
Last Modified:30 Oct 2024 02:40
Publisher:American Statistical Association
ISSN:0003-1305
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1080/00031305.2023.2203177
Project Information:
  • Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
  • Grant ID:
  • Project Title:
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  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)

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