Modern Applied Statistics with S-Plus

Frontmatter

Chapter 1. Introduction

Abstract

Statistics is fundamentally concerned with the understanding of structures in data. One of the effects of the information-technology era has been to make it much easier to collect extensive datasets with minimal human intervention. Fortunately the same technological advances allow the users of statistics access to much more powerful ‘calculators’ to manipulate and display data. This book is about the modern developments in applied statistics which have been made possible by the widespread availability of workstations with high-resolution graphics and computational power equal to a mainframe of a few years ago. Workstations need software, and the S system developed at AT&T’s Bell Laboratories provides a very flexible and powerful environment in which to implement new statistical ideas. Thus this book provides both an introduction to the use of S and a course in modern statistical methods.

W. N. Venables, B. D. Ripley

Chapter 2. The S Language

Abstract

S is a language for the manipulation of objects. It aims to be both an interactive language (like, for example, a Unix shell language) as well as a complete programming language with some convenient object-oriented features. In this chapter we shall be concerned with the interactive language, and hence certain language constructs used mainly in programming will be postponed to Chapter 4.

W. N. Venables, B. D. Ripley

Chapter 3. Graphical Output

Abstract

S-PLUS provides comprehensive graphics facilities, from simple facilities for producing common diagnostic plots by plot (object) to fine control over publication-quality graphs. In consequence, the number of graphics parameters is huge. In this chapter, we build up the complexity gradually. Most readers will not need to go beyond the first 3 sections, and indeed the material later in this chapter is not used elsewhere in this book. However, we have needed to make use of it, especially in matching existing graphical styles.

W. N. Venables, B. D. Ripley

Chapter 4. Programming in S

Abstract

The S language is both an interactive language and a language for adding new functions to the S system. It is a complete programming language with control structures, recursion and a useful variety of data types. The S environment provides many functions to handle standard operations, but most users need occasionally to write new functions. This chapter is concerned with designing, writing, testing and correcting your own S functions.

W. N. Venables, B. D. Ripley

Chapter 5. Distributions and Data Summaries

Abstract

In this chapter we cover a number of topics from classical univariate statistics. Many of the functions used are S-PLUS extensions to S.

W. N. Venables, B. D. Ripley

Chapter 6. Linear Statistical Models

Abstract

Linear models form the core of classical statistics, and S provides extensive facilities to fit and manipulate them. These work with a version of the Wilkinson-Rogers syntax (Wilkinson & Rogers, 1973) for specifying models which we discuss in the Section 6.2, and which is also used for generalized linear models, models for survival analysis and tree-based models in later chapters. The main function for fitting linear models is lm, which provides our first example of a style of S functions we shall see repeatedly in later chapters, producing a fitted model object which is then analysed by generic functions.

W. N. Venables, B. D. Ripley

Chapter 7. Generalized Linear Models

Abstract

Generalized linear models (GLMs) extend linear models to accommodate both non-normal response distributions and transformations to linearity. (We will assume that Chapter 6 has been read before this chapter.) The essay by Firth (1991) gives a good introduction to GLMs; the comprehensive reference is McCullagh & Neider (1989).

W. N. Venables, B. D. Ripley

Chapter 8. Robust Statistics

Abstract

Outliers are sample values which cause surprise in relation to the majority of the sample. This is not a pejorative term; outliers may be correct, but they should always be checked for transcription errors. They can play havoc with standard statistical methods, and many robust and resistant methods have been developed since 1960 to be less sensitive to outliers.

W. N. Venables, B. D. Ripley

Chapter 9. Non-linear Regression Models

Abstract

In linear regression the mean surface in sample space is a plane. In non-linear regression the mean surface may be an arbitrary curved surface but in other respects the models are similar. In practice the mean surface in most non-linear regression models will be approximately planar in the region(s) of high likelihood allowing good approximations based on linear regression techniques to be used. Non-linear regression models can still present tricky computational and inferential problems. (Indeed, the examples here exceeded the capacity of S-PLUS for Windows 3.1.)

W. N. Venables, B. D. Ripley

Chapter 10. Modern Regression

Abstract

S-PLUS has a ‘Modern Regression Module’ which contains functions for a number of regression methods. These are not necessarily non-linear in the sense of Chapter 9, which refers to a non-linear parametrization, but they do allow nonlinear functions of the independent variables to be chosen by the procedures. The methods are all fairly computer-intensive, and so are only feasible in the era of plentiful computing power (and hence are ‘modern’). Some of these methods are part of the S modelling language, and others have been added by S-PLUS. As the latter predate the modelling language and have not been updated, the functions of this chapter do not have a consistent style and user interface.

W. N. Venables, B. D. Ripley

Chapter 11. Survival Analysis

Abstract

Survival analysis is not part of S, but has been added to S-PLUS based on functions written by Terry Therneau (Mayo Foundation) and available as survival2 code from statlib (see Appendix D for further information.) The functions in survival3 were released in mid-1992. They are not part of S-PLUS 3.2, but are scheduled to be included in late 1994. As these functions are much easier to use and provide a higher capability, this chapter is based on their use. (This does mean that the methods are probably not accessible to Windows users at present, as the library uses C code. Section 11.6 sketches how to use survival2, for those who have no other choice.)

W. N. Venables, B. D. Ripley

Chapter 12. Multivariate Analysis

Abstract

Multivariate analysis is concerned with datasets which have more than one response variable for each observational or experimental unit. The datasets can be summarized by data matrices X with n rows and p columns, the rows representing the observations or cases, and the columns the variables. The matrix can be viewed either way, depending whether the main interest is in the relationships between the cases or between the variables. Note that for consistency we represent the variables of a case by the row vector x.

W. N. Venables, B. D. Ripley

Chapter 13. Tree-based Methods

Abstract

The use of tree-based models will be relatively unfamiliar to statisticians, although researchers in other fields have found trees to be an attractive way to express knowledge and aid decision-making. Keys such as Figure 13.1 are common in botany and in medical decision-making, and provide a way to encapsulate and structure the knowledge of experts to be used by less-experienced users. Notice how this tree uses both categorical variables and splits on continuous variables.

W. N. Venables, B. D. Ripley

Chapter 14. Time Series

Abstract

There are now a large number of books on time series. Our philosophy and notation are close to those of the applied book by Diggle (1990) (from which some of our examples are taken). Brockwell and Davis (1991) and Priestley (1981) provide more theoretical treatments, and Bloomfield (1976) and Priestley are particularly thorough on spectral analysis.

W. N. Venables, B. D. Ripley

Chapter 15. Spatial Statistics

Abstract

Spatial statistics is a recent and graphical subject which is ideally suited to implementation in S; S itself includes one spatial interpolation method, akima, and loess which can be used for two-dimensional smoothing, but the specialist methods of spatial statistics have been added and are given in our library spatial. The main references for spatial statistics are Ripley (1981, 1988), Diggle (1983), Upton & Fingleton (1985) and Cressie (1991). Not surprisingly, our notation is closest to Ripley (1981).

W. N. Venables, B. D. Ripley

Backmatter