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.
This text provides a state-of-the-art treatment of distributional regression, accompanied by real-world examples from diverse areas of application. Maximum likelihood, Bayesian and machine learning approaches are covered in-depth and contrasted, providing an integrated perspective on GAMLSS for researchers in statistics and other data-rich fields.
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'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
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A comprehensive presentation of generalized additive models for location, scale and shape linking methods with diverse applications.
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.
Mikis D. Stasinopoulos is Professor of Statistics at the School of Computing and Mathematical Sciences, University of Greenwich. He is, together with Professor Bob Rigby, coauthor of the original Royal Statistical Society article on GAMLSS. He has also coauthored three books on distributional regression, and in particular the theoretical and computational aspects of the GAMLSS framework. Thomas Kneib is a Professor of Statistics at the University of Göttingen, Germany, where he is the Spokesperson of the interdisciplinary Centre for Statistics and Vice-Spokesperson of the Campus Institute Data Science. His main research interests include semiparametric regression, spatial statistics, and distributional regression. Nadja Klein is Emmy Noether Research Group Leader in Statistics and Data Science and Professor for Uncertainty Quantification and Statistical Learning at TU Dortmund University and the Research Center Trustworthy Data Science and Security. Nadja is member of the Junge Akademie and associate editor for 'Biometrics,' 'JABES,' and 'Dependence Modeling.' Her. Her research interests include Bayesian methods, statistical and machine learning, and spatial statistics. Andreas Mayr is a Professor at the Institute for Medical Biometry, Informatics, and Epidemiology at the University of Bonn, Germany. He has authored more than 100 research articles both in statistics as well as medical research and is currently Editor of the 'Statistical Modelling Journal,' Associate Editor of the 'International Journal of Biostatistics,' and Editorial Board Member of the 'International Journal of Eating Disorders.' Gillian Z. Heller is Professor of Biostatistics at the NHMRC Clinical Trials Centre, University of Sydney. She has coauthored four books in the regression modelling area, the first directed towards actuarial applications of the generalized linear model, and the remaining three focussing on distributional regression, in particular the GAMLSS framework.
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