AN INTRODUCTION TO GENERALIZED LINEAR MODELS SECOND ebook 电子书代购

AN INTRODUCTION TO GENERALIZED LINEAR MODELS SECOND ebook 电子书代购
Contents
Preface
1 Introduction
1.1 Background
1.2 Scope
1.3 Notation
1.4 Distributions related to the Normal distribution
1.5 Quadratic forms
1.6 Estimation
1.7 Exercises
2 Model Fitting
2.1 Introduction
2.2 Examples
2.3 Some principles ofstatistica l modelling
2.4 Notation and coding for explanatory variables
2.5 Exercises
3 Exponential Family and Generalized Linear Models
3.1 Introduction
3.2 Exponential family of distributions
3.3 Properties ofdistribution s in the exponential family
3.4 Generalized linear models
3.5 Examples
3.6 Exercises
4 Estimation
4.1 Introduction
4.2 Example: Failure times for pressure vessels
4.3 Maximum likelihood estimation
4.4 Poisson regression example
4.5 Exercises
5 Inference
5.1 Introduction
5.2 Sampling distribution for score statistics
? 2002 by Chapman & Hall/CRC
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5.3 Taylor series approximations
5.4 Sampling distribution for maximum likelihood estimators
5.5 Loglikelihood ratio statistic
5.6 Sampling distribution for the deviance
5.7 Hypothesis testing
5.8 Exercises
6 Normal Linear Models
6.1 Introduction
6.2 Basic results
6.3 Multiple linear regression
6.4 Analysis of variance
6.5 Analysis ofc ovariance
6.6 General linear models
6.7 Exercises
7 Binary Variables and Logistic Regression
7.1 Probability distributions
7.2 Generalized linear models
7.3 Dose response models
7.4 General logistic regression model
7.5 Goodness offi t statistics
7.6 Residuals
7.7 Other diagnostics
7.8 Example: Senility and WAIS
7.9 Exercises
8 Nominal and Ordinal Logistic Regression
8.1 Introduction
8.2 Multinomial distribution
8.3 Nominal logistic regression
8.4 Ordinal logistic regression
8.5 General comments
8.6 Exercises
9 Count Data, Poisson Regression and LogLinear Models
9.1 Introduction
9.2 Poisson regression
9.3 Examples ofco ntingency tables
9.4 Probability models for contingency tables
9.5 Loglinear models
9.6 Inference for loglinear models
9.7 Numerical examples
9.8 Remarks
9.9 Exercises
? 2002 by Chapman & Hall/CRC
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10 Survival Analysis
10.1 Introduction
10.2 Survivor functions and hazard functions
10.3 Empirical survivor function
10.4 Estimation
10.5 Inference
10.6 Model checking
10.7 Example: remission times
10.8 Exercises
11 Clustered and Longitudinal Data
11.1 Introduction
11.2 Example: Recovery from stroke
11.3 Repeated measures models for Normal data
11.4 Repeated measures models for nonNormal data
11.5 Multilevel models
11.6 Stroke example continued
11.7 Comments
11.8 Exercises
Software
References
? 2002 by Chapman & Hall/CRC
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Preface
Statistical tools for analyzing data are developing rapidly so that the 1990
edition ofthis book is now out ofdate.
The original purpose ofthe book was to present a unified theoretical and
conceptual framework for statistical modelling in a way that was accessible
to undergraduate students and researchers in other fields. This new edition
has been expanded to include nominal (or multinomial) and ordinal logistic
regression, survival analysis and analysis oflongitudinal and clustered data.
Although these topics do not fall strictly within the definition of generalized
linear models, the underlying principles and methods are very similar and
their inclusion is consistent with the original purpose ofthe book.
The new edition relies on numerical methods more than the previous edition
did. Some ofthe calculations can be performed with a spreadsheet while others
require statistical software. There is an emphasis on graphical methods for
exploratory data analysis, visualizing numerical optimization (for example,
ofthe likelihood function) and plotting residuals to check the adequacy of
models.
Introduction
1.1 Background
This book is designed to introduce the reader to generalized linear models;
these provide a unifying framework for many commonly used statistical techniques.
They also illustrate the ideas ofstatistical modelling.
The reader is assumed to have some familiarity with statistical principles
and methods. In particular, understanding the concepts ofestimation, sampling
distributions and hypothesis testing is necessary. Experience in the use
ofttests, analysis ofv ariance, simple linear regression and chisquared tests of
independence for twodimensional contingency tables is assumed. In addition,
some knowledge ofmatrix algebra and calculus is required.
The reader will find it necessary to have access to statistical computing
facilities. Many statistical programs, languages or packages can now perform
the analyses discussed in this book. Often, however, they do so with a different
program or procedure for each type of analysis so that the unifying structure
is not apparent.
Some programs or languages which have procedures consistent with the
approach used in this book are: Stata, SPLUS, Glim, Genstat and SYSTAT.
This list is not comprehensive as appropriate modules are continually
being added to other programs.
In addition, anyone working through this book may find it helpful to be able
to use mathematical software that can perform matrix algebra, differentiation
and iterative calculations.
1.2 Scope
The statistical methods considered in this
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