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E-raamat: Introduction to Categorical Data Analysis

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(University of Florida, Gainesville)
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A valuable new edition of a standard reference

The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data.

Adding to the value in the new edition is:

• Illustrations of the use of R software to perform all the analyses in the book

• A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis

• New sections in many chapters introducing the Bayesian approach for the methods of that chapter

• More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets

• An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises

Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more.

An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.

Preface ix
About the Companion Website xiii
1 Introduction
1(24)
1.1 Categorical Response Data
1(2)
1.2 Probability Distributions for Categorical Data
3(2)
1.3 Statistical Inference for a Proportion
5(5)
1.4 Statistical Inference for Discrete Data
10(3)
1.5 Bayesian Inference for Proportions *
13(4)
1.6 Using R Software for Statistical Inference about Proportions *
17(4)
Exercises
21(4)
2 Analyzing Contingency Tables
25(40)
2.1 Probability Structure for Contingency Tables
26(3)
2.2 Comparing Proportions in 2 × 2 Contingency Tables
29(2)
2.3 The Odds Ratio
31(5)
2.4 Chi-Squared Tests of Independence
36(6)
2.5 Testing Independence for Ordinal Variables
42(4)
2.6 Exact Frequentist and Bayesian Inference *
46(6)
2.7 Association in Three-Way Tables
52(4)
Exercises
56(9)
3 Generalized Linear Models
65(24)
3.1 Components of a Generalized Linear Model
66(2)
3.2 Generalized Linear Models for Binary Data
68(4)
3.3 Generalized Linear Models for Counts and Rates
72(4)
3.4 Statistical Inference and Model Checking
76(6)
3.5 Fitting Generalized Linear Models
82(2)
Exercises
84(5)
4 Logistic Regression
89(34)
4.1 The Logistic Regression Model
89(5)
4.2 Statistical Inference for Logistic Regression
94(4)
4.3 Logistic Regression with Categorical Predictors
98(4)
4.4 Multiple Logistic Regression
102(5)
4.5 Summarizing Effects in Logistic Regression
107(3)
4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation
110(3)
Exercises
113(10)
5 Building and Applying Logistic Regression Models
123(36)
5.1 Strategies in Model Selection
123(7)
5.2 Model Checking
130(6)
5.3 Infinite Estimates in Logistic Regression
136(4)
5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression *
140(5)
5.5 Alternative Link Functions: Linear Probability and Probit Models *
145(5)
5.6 Sample Size and Power for Logistic Regression *
150(1)
Exercises
151(8)
6 Multicategory Logit Models
159(34)
6.1 Baseline-Category Logit Models for Nominal Responses
159(8)
6.2 Cumulative Logit Models for Ordinal Responses
167(9)
6.3 Cumulative Link Models: Model Checking and Extensions *
176(8)
6.4 Paired-Category Logit Modeling of Ordinal Responses *
184(3)
Exercises
187(6)
7 Loglinear Models for Contingency Tables and Counts
193(34)
7.1 Loglinear Models for Counts in Contingency Tables
194(6)
7.2 Statistical Inference for Loglinear Models
200(7)
7.3 The Loglinear -- Logistic Model Connection
207(3)
7.4 Independence Graphs and Collapsibility
210(4)
7.5 Modeling Ordinal Associations in Contingency Tables
214(3)
7.6 Loglinear Modeling of Count Response Variables *
217(4)
Exercises
221(6)
8 Models for Matched Pairs
227(26)
8.1 Comparing Dependent Proportions for Binary Matched Pairs
228(2)
8.2 Marginal Models and Subject-Specific Models for Matched Pairs
230(5)
8.3 Comparing Proportions for Nominal Matched-Pairs Responses
235(4)
8.4 Comparing Proportions for Ordinal Matched-Pairs Responses
239(4)
8.5 Analyzing Rater Agreement *
243(4)
8.6 Bradley-Terry Model for Paired Preferences *
247(2)
Exercises
249(4)
9 Marginal Modeling of Correlated, Clustered Responses
253(20)
9.1 Marginal Models Versus Subject-Specific Models
254(1)
9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach
255(5)
9.3 Marginal Modeling for Clustered Multinomial Responses
260(3)
9.4 Transitional Modeling, Given the Past
263(3)
9.5 Dealing with Missing Data *
266(2)
Exercises
268(5)
10 Random Effects: Generalized Linear Mixed Models
273(26)
10.1 Random Effects Modeling of Clustered Categorical Data
273(5)
10.2 Examples: Random Effects Models for Binary Data
278(6)
10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms
284(4)
10.4 Multilevel (Hierarchical) Models
288(3)
10.5 Latent Class Models *
291(4)
Exercises
295(4)
11 Classification and Smoothing *
299(26)
11.1 Classification: Linear Discriminant Analysis
300(2)
11.2 Classification: Tree-Based Prediction
302(4)
11.3 Cluster Analysis for Categorical Responses
306(4)
11.4 Smoothing: Generalized Additive Models
310(3)
11.5 Regularization for High-Dimensional Categorical Data (Large p)
313(8)
Exercises
321(4)
12 A Historical Tour of Categorical Data Analysis *
325(6)
Appendix: Software for Categorical Data Analysis 331(18)
A.1 R for Categorical Data Analysis
331(1)
A.2 SAS for Categorical Data Analysis
332(10)
A.3 Stata for Categorical Data Analysis
342(4)
A.4 SPSS for Categorical Data Analysis
346(3)
Brief Solutions to Odd-Numbered Exercises 349(14)
Bibliography 363(2)
Examples Index 365(4)
Subject Index 369
ALAN AGRESTI is Distinguished Professor Emeritus at the University of Florida. He has presented short courses on categorical data methods in 35 countries. He is the author of seven books, including the bestselling Categorical Data Analysis (Wiley), Foundations of Linear and Generalized Linear Models (Wiley), Statistics: The Art and Science of Learning from Data (Pearson), and Statistical Methods for the Social Sciences (Pearson).
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