The place of probability distributions in statistical learning. A commented book review of ‘Distributions for modeling location, scale, and shape using GAMLSS in R’ by Rigby et al. (2021)

Abstract

Generalised additive models for location, scale and shape (GAMLSS) is a type of distributional regression framework that enables modelling numeric dependent variables via probability distributions other than those of the exponential family. While the cogs behind GAMLSS are provided in Stasinopoulos et al. 2017's book ‘Flexible regression and smoothing using GAMLSS in R, the new book by Rigby et al. considers the distributions implemented in the R software that are usable for GAMLSS modelling. A commented summary of that second book is provided in a supplementary file. Unlike traditional book reviews, two topics in this new book are briefly elaborated on: robustness (Chapter 12) and shape (Chapters 14–16). It is concluded that despite GAMLSS being a powerful and flexible framework for supervised statistical learning, striving for interpretable GAMLSS models is essential.