Nature Reviews Primer: Distributional Regression
Most statistical models ask how explanatory variables affect the mean of a response. But in many applications, the interesting questions go far beyond the average: Does variability increase? Are extremes becoming more likely? Does the distribution become more skewed?
Our new Nature Reviews Primer provides a comprehensive introduction to distributional regression, with a particular focus on Generalized Additive Models for Location, Scale and Shape (GAMLSS). Rather than modeling only the expected value, distributional regression allows every aspect of a probability distribution, including variance, skewness, tail behavior, and zero inflation, to depend on explanatory variables. This enables richer inference, improved uncertainty quantification, and direct prediction of quantities such as conditional quantiles and exceedance probabilities.
What the Primer Covers
Why move beyond the mean?
We discuss why variability often contains important scientific information and how modeling full conditional distributions can reveal patterns that classical regression models miss.The GAMLSS framework
We introduce the mathematical foundations of GAMLSS, explain how to choose suitable response distributions, specify regression models for multiple distributional parameters, estimate models, and perform diagnostic checks.Interpreting distributional models
The Primer demonstrates how to understand effects on variance, skewness, quantiles, prediction intervals, and exceedance probabilities—not just the conditional mean.Applications across scientific disciplines
Case studies from ecology, environmental science, and health research illustrate how distributional regression improves risk assessment, probabilistic prediction, and scientific interpretation.
Unlike a methodological research article, this Primer is intended as a practical guide for researchers who want to understand when and how to apply distributional regression in practice. We hope it serves as an accessible entry point for anyone interested in moving from mean-based modeling to full probabilistic modeling.