1st Edition

Statistical Models in S

Edited By J. M. Chambers, T.J. Hastie Copyright 1992
    624 Pages
    by Chapman & Hall

    Statistical Models in S extends the S language to fit and analyze a variety of statistical models, including analysis of variance, generalized linear models, additive models, local regression, and tree-based models. The contributions of the ten authors-most of whom work in the statistics research department at AT&T Bell Laboratories-represent results of research in both the computational and statistical aspects of modeling data.

    1 An Appetizer

    John M. Chambers, Trevor J. Hastie

    A Manufacturing Experiment

    Models for the Experimental Results

    A Second Experiment


    2 Statistical Models

    John M. Chambers, Trevor J. Hastie

    Thinking About Models

    Models and Data

    Creating Statistical Models

    Model Formulas in S

    Data of Different Types in Formulas


    Combining Data and Formula

    More on Models

    Formulas in Detail

    Coding Factors by Contrasts

    Internal Organization of Models

    Rules for Coding Expanded Formulas

    Formulas and Terms

    Terms and the Model Matrix

    Bibliographic Notes

    Data for Mdels

    John M. Chambers

    Examples of Data Frames

    Example: Automobile Data

    Example: A Manufacturing Experiment

    Example: A Marketing Study

    Computations on Data Frames

    Variables in Data Frames; Factors

    Creating Data Frames

    Using and Modifying Data Frames

    Summaries and Plots

    Advanced Computations on Data

    Methods for Data Frames

    Data Frames as Databases or Evaluation Frames

    Model Frames and Model Matrices

    Parameterized Data Frames

    4 Linear Models

    John M. Chambers

    Linear Models in Statistics

    S Functions and Objects

    Fitting the Model

    Basic Summaries


    Options in Fitting

    Updating Models

    Specializing and Extending the Computations

    Repeated Fitting of Similar Models

    Adding and Dropping Terms

    Influence of Individual Observations

    Numerical and Statistical Methods

    Mathematical and Statistical Results

    Numerical Methods

    Overdetermined and Ill-determined Models

    5 Analysis of Variance; Designed Experiments

    John M. Chambers, Anne E. Freeny, Richard M. Heiberger

    Models for Experiments: The Analysis of Variance

    S Functions and Objects

    Analysis of Variance Models

    Graphical Methods and Diagnostics

    Generating Designs

    The S Functions: Advanced Use

    Parameterization; Contrasts

    More on Aliasing

    Anova Models as Projections

    Computational Techniques

    Basic Computational Theory Aliasing; Rank-deficiency

    Error Terms

    Computations for Projection

    6 Generalized Linear Models

    Trevor J. Hastie, Daryl Pregibon

    Statistical Methods

    S Functions and Objects

    Fitting the Model

    Specifying the Link and Variance Functions

    Updating Models

    Analysis of Deviance Tables

    Chi-squared Analyses


    Specializing and Extending the Computations

    Other Arguments to glm()

    Coding Factors for GLMs

    More on Families

    Diagnostics Stepwise Model Selection


    Statistical and Numerical Methods

    Likelihood Inference

    Quadratic Approximations


    Initial Values

    7 Generalized Additive Models

    Trevor J. Hastie

    Statistical Methods

    Data Analysis and Additive Models

    Fitting Generalized Additive Models

    S Functions and Objects

    Fitting the Models

    Plotting the Fitted Models

    Further Details on gam()

    Parametric Additive Models: bs() and ns()

    An Example in Detail

    Specializing and Extending the Computations

    Stepwise Model Selection

    Missing Data


    Smoothers in gam()

    More on Plotting

    Numerical and Computational Details

    Scatterplot Smoothing

    Fitting Simple Additive Models

    Fitting Generalized Additive Models

    Standard Errors and Degrees of Freedom

    Implementation Details

    8 Local Regression Models

    William S. Cleveland, Eric Grosse, William M. Shyu

    Statistical Models and Fitting

    Definition of Local Regression Models

    Loess: Fitting Local Regression Models

    S Functions and Objects

    Gas Data

    Ethanol Data

    Air Data

    Galaxy Velocities

    Fuel Comparison Data

    Specializing and Extending the Computations




    Statistical and Computational Methods

    9 Tree-Based Models

    Linda A. Clark, Daryl Pregibon

    Tree-Based Models in Statistics

    Numeric Response and a Single Numeric Predictor

    Factor Response and Numeric Predictions

    Factor Response and Mixed Predictor Variables

    S Functions and Objects

    Growing a Tree

    Functions for Diagnostics

    Examining Subtrees

    Examining Nodes

    Examining Splits

    Examining Leaves

    Specializing the Computations

    Numerical and Statistical Methods

    Handling Missing Values

    Some Computational Issues

    Extending the Computations

    10 Nonlinear Models

    Douglas M. Bates, John M. Chambers

    Statistical Methods

    S Functions

    Fitting the Models



    Profiling the Objective Function

    Partially Linear Models

    Some Details

    Controlling the Fitting

    Examining the Model

    Weighted Nonlinear Regression

    Programming Details

    Optimization Algorithm

    Nonlinear Least-Squares Algorithm

    A Classes and Methods: Object-oriented Programming in S

    John M. Chambers

    A.1 Motivation

    A.2 Background

    A.3 The Mechanism

    A.4 An Example of Designing a Class

    A.5 Inheritance

    A.6 The Frames for Methods

    A.7 Group Methods; Methods for Operators

    A.8 Replacement Methods

    A.9 Assignment Methods

    A.10 Generic Functions

    A.11 Comment

    B S Functions and Classes




    Hastie, T.J.