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2018 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Semiparametric Regression with R

verfasst von: Jaroslaw Harezlak, Dr. David Ruppert, Matt P. Wand

Verlag: Springer New York

Buchreihe : Use R!

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This easy-to-follow applied book on semiparametric regression methods using R is intended to close the gap between the available methodology and its use in practice. Semiparametric regression has a large literature but much of it is geared towards data analysts who have advanced knowledge of statistical methods. While R now has a great deal of semiparametric regression functionality, many of these developments have not trickled down to rank-and-file statistical analysts.
The authors assemble a broad range of semiparametric regression R analyses and put them in a form that is useful for applied researchers. There are chapters devoted to penalized spines, generalized additive models, grouped data, bivariate extensions of penalized spines, and spatial semi-parametric regression models. Where feasible, the R code is provided in the text, however the book is also accompanied by an external website complete with datasets and R code. Because of its flexibility, semiparametric regression has proven to be of great value with many applications in fields as diverse as astronomy, biology, medicine, economics, and finance. This book is intended for applied statistical analysts who have some familiarity with R.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Regression is used to understand the relationships between predictor variables and response variables and for predicting the latter using the former. In parametric regression, the effect of each predictor has a simple form, for example, is a linear or exponential function, so that its overall shape is dictated by the model, not the data. In contrast, with nonparametric regression the model is flexible enough to allow any smooth trend in the data; see Fig. 1.1 for an example.
Jaroslaw Harezlak, David Ruppert, Matt P. Wand
Chapter 2. Penalized Splines
Abstract
In this chapter, we study nonparametric regression with a single continuous predictor. This problem is often called scatterplot smoothing. Our emphasis is on the use of penalized splines. We also show that a penalized spline model can be represented as a linear mixed model, which allows us to fit penalized splines using linear mixed model software.
Jaroslaw Harezlak, David Ruppert, Matt P. Wand
Chapter 3. Generalized Additive Models
Abstract
The models fit in Chap. 2 have two limitations. First, the conditional distribution of the response, given the predictors, is assumed to be Gaussian. Second, only a single predictor is allowed to have a smooth nonlinear effect—the other predictors are modeled linearly. The first limitation is addressed by using generalized linear models (GLMs), which remove the Gaussian assumption and allow the response variable to have other distributions such as those within the Binomial and Poisson families.
Jaroslaw Harezlak, David Ruppert, Matt P. Wand
Chapter 4. Semiparametric Regression Analysis of Grouped Data
Abstract
Grouped data arise in several diverse contexts in statistical design and analysis. Examples include medical studies in which patients are followed over time and measurements on them recorded repeatedly, educational studies in which students grouped into classrooms and schools are scored on examinations, and sample surveys in which the respondents to questionnaires are grouped within geographical districts.
Jaroslaw Harezlak, David Ruppert, Matt P. Wand
Chapter 5. Bivariate Function Extensions
Abstract
We now focus on models for the joint effect of two continuous predictor variables. Additive models are convenient, but there is no reason to assume that they are always adequate. In the general bivariate models studied in this chapter, the joint effect of the two variables is a smooth, but otherwise unrestricted, function of these variables. Therefore, these models allow interactions so that the effect of one predictor depends upon the value of the other predictor.
Jaroslaw Harezlak, David Ruppert, Matt P. Wand
Chapter 6. Selection of Additional Topics
Abstract
Chapters 2–5 deal with the most fundamental semiparametric regression topics and implementation in R. There are numerous other topics but, of course, not all of them can be covered in a single book. Instead we cover a selection of additional topics in this final chapter that we feel are worthy of some mention. These concern robust and quantile regression, functional data, kernel machines and classification, missing data, and measurement error.
Jaroslaw Harezlak, David Ruppert, Matt P. Wand
Backmatter
Metadaten
Titel
Semiparametric Regression with R
verfasst von
Jaroslaw Harezlak
Dr. David Ruppert
Matt P. Wand
Copyright-Jahr
2018
Verlag
Springer New York
Electronic ISBN
978-1-4939-8853-2
Print ISBN
978-1-4939-8851-8
DOI
https://doi.org/10.1007/978-1-4939-8853-2