Generalized Additive Models for Location, Scale and Shape
A Distributional Regression Approach, with Applications

A comprehensive presentation of generalized additive models for location, scale and shape linking methods with diverse applications.

Mikis D. Stasinopoulos (Author), Thomas Kneib (Author), Nadja Klein (Author), Andreas Mayr (Author), Gillian Z. Heller (Author)

9781009410069, Cambridge University Press

Hardback, published 29 February 2024

306 pages
26.2 x 18.5 x 2.2 cm, 0.77 kg

'In a relatively short time, GAMLSS has become very popular. The driving force was the quality of the R package that made this powerful model easily accessible for applied statisticians. Despite the popularity of the model, the literature on GAMLSS is relatively small. This book fills a gap: it carefully presents the existing theory and adds extensions like Bayesian inference and boosting as well as new tools for interpreting GAMLSS models. In addition, it contains a large section with new and inspiring applications.' Paul Eilers, Erasmus University Medical Center, Rotterdam, the Netherlands

An emerging field in statistics, distributional regression facilitates the modelling of the complete conditional distribution, rather than just the mean. This book introduces generalized additive models for location, scale and shape (GAMLSS) – one of the most important classes of distributional regression. Taking a broad perspective, the authors consider penalized likelihood inference, Bayesian inference, and boosting as potential ways of estimating models and illustrate their usage in complex applications. Written by the international team who developed GAMLSS, the text's focus on practical questions and problems sets it apart. Case studies demonstrate how researchers in statistics and other data-rich disciplines can use the model in their work, exploring examples ranging from fetal ultrasounds to social media performance metrics. The R code and data sets for the case studies are available on the book's companion website, allowing for replication and further study.

Preface
Notation and Termanology
Part I. Introduction and Basics: 1. Distributional Regression Models
2. Distributions
3. Additive Model Terms
Part II. Statistical Inference in GAMLSS: 4. Inferential Methods
5. Penalized Maximum Likelihood Inference
6. Bayesian Inference
7. Statistical Boosting for GAMLSS
Part. III Applications and Case Studies: 8. Fetal Ultrasound
9. Speech Intelligibility Testing
10. Social Media Post Performance
11. Childhood Undernutrition in India
12. Socioeconomic Determinants of Federal Election Outcomes in Germany
13. Variable Selection for Gene Expression Data
Appendix A. Continuous Distributions
Appendix B. Discrete Distributions
Bibliography
Index.

Subject Areas: Probability & statistics [PBT]