Merder, Julian ORCID: https://orcid.org/0000-0002-5958-7016, Rigby, Robert A. ORCID: https://orcid.org/0000-0003-4787-623X, Mayr, Andreas ORCID: https://orcid.org/0000-0001-7106-9732, Heller, Gillian Z. ORCID: https://orcid.org/0000-0003-1270-1499, Kneib, Thomas ORCID: https://orcid.org/0000-0003-3390-0972, Umlauf, Nikolaus ORCID: https://orcid.org/0000-0003-2160-9803, De Bastiani, Fernanda ORCID: https://orcid.org/0000-0001-8532-639X, Stauffer, Reto ORCID: https://orcid.org/0000-0002-3798-5507, Tonkin, Jonathan D. ORCID: https://orcid.org/0000-0002-6053-291X, Logothetis, Nikos, Zeileis, Achim ORCID: https://orcid.org/0000-0003-0918-3766 and Stasinopoulos, Dimitrios M. (2026) Distributional regression using generalized additive models for location, scale and shape. Nature Reviews Methods Primers, 6:49. ISSN 2662-8449 (Online) (doi:10.1038/s43586-026-00498-z)

PDF (Author's Accepted Manuscript) 54340 RIGBY_Distributional_Regression_Using_Generalized_Additive_Models_For_Location_(AAM)_2026.pdf - Accepted Version Restricted to Repository staff only until 9 January 2027. Download (1MB) | Request a copy

Abstract

Distributional regression (DR) encompasses regression methods that model the entire probability distribution of the outcome (response variable) conditional on explanatory variables. Generalized additive models for location, scale, and shape (GAMLSS) represent the most common framework of DR and extend traditional regression models, such as linear models, generalized linear models, and generalized additive models, by allowing not only the mean, but also other characteristics of the response distribution, like variance, skewness, and tail behaviour, to be modelled as functions of explanatory variables. This allows direct assessment of how explanatory variables influence variability, quantiles, and exceedance probabilities, thereby providing deeper insight into the underlying data-generating process. This makes DR ideal for applications where predicting uncertainty and extreme events, and hence risk assessment, is critical. In this Primer, we provide an overview of DR with a comprehensive focus on GAMLSS, including the theoretical background and guidelines for practical implementation and model checking. Using case studies from multiple scientific fields, we demonstrate how GAMLSS captures changes in distributional features that are intrinsic to natural systems but frequently overlooked by classical regression and machine learning approaches focused on conditional means. Finally, we highlight future directions, particularly combining DR with machine learning.

Item Type:	Article
Uncontrolled Keywords:	distributional regression, GAMLSS, exceedance probabilities, quantile estimation, centile estimation, prediction interval estimation, predictions beyond the mean
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified:	04 Sep 2026 08:46
URI:	https://gala.gre.ac.uk/id/eprint/54340

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