This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent.
In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables.
- Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R.
- Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning.
- R code integrated into the text for ease of understanding and replication.
- Supplemented by a website with code, data and extra materials.
This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.
Table of Contents
Part I Introduction to models and packages
Introduction to the gamlss packages
Part II The R implementation: algorithms and functions
The gamlss() function
Methods for fitted gamlss objects
Part III Distributions
The gamlss.family of distributions
Finite mixture distributions
Part IV Additive terms
Linear parametric additive terms
Additive Smoothing Terms
Part V Model selection and diagnostics
Model selection techniques
Part VI Applications
Mikis D. Stasinopoulos, Robert A. Rigby, Gillian Z. Heller, Vlasios Voudouris, Fernanda De Bastiani
Featured Author Profiles
"That the authors succeed in communicating the process of learning from data using the GAMLSS suite of tool is due to the clear and effective organization of the book. The book is a complete introduction to GAMLSS models (and by extension GLMs and GAMs) as well as some newer techniques such as semi-parametric neural networks/deep learning and trees. I highly recommend it to any reader interested in advanced machine learning techniques."
—Carlo Di Maio, European Central Bank
"’Flexible Regression and Smoothing: Using GAMLSS in R’ is a comprehensive and authoritative text from the co-authors of perhaps the most flexible regression modeling framework in statistics and supervised machine learning. Traditional regression approaches focus on the mean of the distribution conditional on a set of predictor variables. GAMLSS extends this up to four distribution parameters which are modeled as additive functions of predictor variables. Through this extension, the analyst has a choice of over 90 continuous, discrete and mixed distributions for the response variable which allows modeling of highly skewed and kurtotic distributions while improving transparency and interpretability for the effects of predictor variables driving the model. This well-written book details the methodology and R packages underlying the framework including algorithms, model fitting, additive terms, model diagnostics and examples with real data. The impact of GAMLSS has been demonstrated in many industries including medicine, environmental science, biology, finance and insurance. Data scientists, quantitative analysts and researchers will be enlightened when discovering the myriad of modeling opportunities through the material in this landmark text."
—Edward Tong, PhD
"Generalized additive models for location, scale, and shape (GAMLSS) as introduced by Bob Rigby and Mikis Stasinopoulos in their seminal 2005 paper are one versatile, yet simple method that allows regression predictors to be placed on any parameter of a potentially complex response distribution. Since 2005, Bob, Mikis, and co-workers invested a considerable amount of work into the development of statistical software for GAMLSS as well as many extensions of the methodology. Flexible Regression and Smoothing: Using GAMLSS in R is a perfect way of getting started with GAMLSS, since it combines an easily accessible overview of the underlying methods with a thorough introduction to the implementation in R via the GAMLSS package family. Moreover, the book also covers many advanced topics such as finite mixture specifications and random effects as well as many areas of applied interest, such as model selection and model diagnostics. It is therefore an invaluable resource both for those interested in applying GAMLSS in practice and those that are interested in the underlying methods. In summary, there is no more excuse to focus on means in regression given the easy access to advanced methods such as GAMLSS through this book."
—Thomas Kneib, Georg-August-Universität Göttingen
"This well-written book is an introduction to Generalised Additive Models for Location, Scale and Shape (GAMLSS) and the use of the R package gamlss developed by the authors for fitting and using these models. The focus is mainly on the R package, making applied statisticians the primary target audience... it contains a lot of information about the package but it does not feel like just a manual... The gamlss package allows smooth functions of explanatory variables to be estimated in various ways, namely, it allows the use of penalised likelihood methods, including ridge regression and the lasso, and also implements fitting finite mixtures of distributions (including zero-inflated and zero-adjusted models as special cases), and centile or quantile estimation. In all of this, the smoothing parameters can be chosen automatically. It is very flexible, and potentially very useful and highly extendable. This is a good reason for looking into the book and considering using the package."
-A.H. Welsh, Australian & New Zealand Journal of Statistics, August 2019