Distributional Regression for Data Analysis

Abstract

Flexible modeling of how an entire distribution changes with covariates is an important yet challenging generalization of mean-based regression that has seen growing interest over the past decades in both the statistics and machine learning literature. This review outlines selected state-of-the-art statistical approaches to distributional regression, complemented with alternatives from machine learning. Topics covered include the similarities and differences between these approaches, extensions, properties and limitations, estimation procedures, and the availability of software. In view of the increasing complexity and availability of large-scale data, this review also discusses the scalability of traditional estimation methods, current trends, and open challenges. Illustrations are provided using data on childhood malnutrition in Nigeria and Australian electricity prices. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Assessing Potential Heteroscedasticity in Psychological Data: A GAMLSS approach

“…Thus, GAMLSS stands as a broader applicable alternative to LM without suffering from the problems that emerge from its fundamental, often non-valid assumptions, such as homoscedasticity. Lastly, it is worth noting that present variations of GAMLSS render it appropriate for machine learning analyses, such as distributional regression trees and forests (see for example, the work of Klein, 2024 andConstable et al, 2023).…”