Flexible Regression and Smoothing

This book provides a broad overview of GAMLSS methodology and how it is implemented in R. It includes a comprehensive collection of real data examples, integrated code, and figures to illustrate the methods, and is supplemented by a website.

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.

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Key Features:

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• 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.

Autorentext

Mikis D. Stasinopoulos, Robert A. Rigby, Gillian Z. Heller, Vlasios Voudouris, Fernanda De Bastiani

Inhalt

Part I Introduction to models and packages

Why GAMLSS?

Introduction to the gamlss packages

Part II The R implementation: algorithms and functions

The Algorithms

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

Random effects

Part V Model selection and diagnostics

Model selection techniques

Diagnostics

Part VI Applications

Centile Estimation

Further Applications