Flexible Regression And Smoothing

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. Key Features: 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.

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. Key Features: 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.

Flexible Bayesian Regression Modeling is a step-by-step guide to the Bayesian revolution in regression modeling, for use in advanced econometric and statistical analysis where datasets are characterized by complexity, multiplicity, and large sample sizes, necessitating the need for considerable flexibility in modeling techniques. It reviews three forms of flexibility: methods which provide flexibility in their error distribution; methods which model non-central parts of the distribution (such as quantile regression); and finally models that allow the mean function to be flexible (such as spline models). Each chapter discusses the key aspects of fitting a regression model. R programs accompany the methods. This book is particularly relevant to non-specialist practitioners with intermediate mathematical training seeking to apply Bayesian approaches in economics, biology, finance, engineering and medicine. Introduces powerful new nonparametric Bayesian regression techniques to classically trained practitioners Focuses on approaches offering both superior power and methodological flexibility Supplemented with instructive and relevant R programs within the text Covers linear regression, nonlinear regression and quantile regression techniques Provides diverse disciplinary case studies for correlation and optimization problems drawn from Bayesian analysis ‘in the wild’

This is a book about statistical distributions, their properties, and their application to modelling the dependence of the location, scale, and shape of the distribution of a response variable on explanatory variables. It will be especially useful to applied statisticians and data scientists in a wide range of application areas, and also to those interested in the theoretical properties of distributions. This book follows the earlier book ‘Flexible Regression and Smoothing: Using GAMLSS in R’, [Stasinopoulos et al., 2017], which focused on the GAMLSS model and software. GAMLSS (the Generalized Additive Model for Location, Scale, and Shape, [Rigby and Stasinopoulos, 2005]), is a regression framework in which the response variable can have any parametric distribution and all the distribution parameters can be modelled as linear or smooth functions of explanatory variables. The current book focuses on distributions and their application. Key features: Describes over 100 distributions, (implemented in the GAMLSS packages in R), including continuous, discrete and mixed distributions. Comprehensive summary tables of the properties of the distributions. Discusses properties of distributions, including skewness, kurtosis, robustness and an important classification of tail heaviness. Includes mixed distributions which are continuous distributions with additional specific values with point probabilities. Includes many real data examples, with R code integrated in the text for ease of understanding and replication. Supplemented by the gamlss website. This book will be useful for applied statisticians and data scientists in selecting a distribution for a univariate response variable and modelling its dependence on explanatory variables, and to those interested in the properties of distributions.

Handbook and reference guide for students and practitioners of statistical regression-based analyses in R Handbook of Regression Analysis with Applications in R, Second Edition is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors’ thorough treatment of “classical” regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data. The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include: Regularization methods Smoothing methods Tree-based methods In the new edition of the Handbook, the data analyst’s toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website. Of interest to undergraduate and graduate students taking courses in statistics and regression, the Handbook of Regression Analysis will also be invaluable to practicing data scientists and statisticians.

This book summarizes the state of the art in generalized linear models (GLMs) and their various extensions: GAMs, mixed models and credibility, and some nonlinear variants (GNMs). In order to deal with tail events, analytical tools from Extreme Value Theory are presented. Going beyond mean modeling, it considers volatility modeling (double GLMs) and the general modeling of location, scale and shape parameters (GAMLSS). Actuaries need these advanced analytical tools to turn the massive data sets now at their disposal into opportunities. The exposition alternates between methodological aspects and case studies, providing numerical illustrations using the R statistical software. The technical prerequisites are kept at a reasonable level in order to reach a broad readership. This is the first of three volumes entitled Effective Statistical Learning Methods for Actuaries. Written by actuaries for actuaries, this series offers a comprehensive overview of insurance data analytics with applications to P&C, life and health insurance. Although closely related to the other two volumes, this volume can be read independently.

This is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable.