An Introduction to Categorical Data Analysis

ISBN-13: 9781119405269 / Angielski / Twarda / 2018 / 400 str.

Gainesville) Agresti Alan (University of Florida

Opis

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.

Spis treści

Preface

1. Introduction

1.1 Categorical Response Data

1.2 Probability Distributions for Categorical Data

1.3 Statistical Inference for a Proportion

1.4 Statistical Inference for Discrete Data

1.5 Bayesian Inference for Proportions

1.6 Using R Software for Statistical Inference about Proportions

Exercises

2. Analyzing Contingency Tables

2.1 Probability Structure for Contingency Tables

2.2 Comparing Proportions in 2×2 Contingency Tables

2.3 The Odds Ratio

2.4 Chi–Squared Tests of Independence

2.5 Testing Independence for Ordinal Variables

2.6 Exact Frequentist and Bayesian Inference

2.7 Association in Three–Way Tables

Exercises

3. Generalized Linear Models

3.1 Components of a Generalized Linear Model

3.2 Generalized Linear Models for Binary Data

3.3 Generalized Linear Models for Counts and Rates

3.4 Statistical Inference and Model Checking

3.5 Fitting Generalized Linear Models

Exercises

4. Logistic Regression

4.1 The Logistic Regression Model

4.2 Statistical Inference for Logistic Regression

4.3 Logistic Regression with Categorical Predictors

4.4 Multiple Logistic Regression

4.5 Summarizing Effects in Logistic Regression

4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation

Exercises

5. Building and Applying Binary Regression Models

5.1 Strategies in Model Selection

5.2 Model Checking

5.3 Infinite Estimates in Logistic Regression

5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression

5.5 Alternative Link Functions: Linear Probability and Probit Models

5.6 Sample Size and Power for Logistic Regression

Exercises

6. Multicategory Logit Models

6.1 Baseline–Category Logit Models for Nominal Responses

6.2 Cumulative Logit Models for Ordinal Responses

6.3 Cumulative Link Models: Model Checking and Extensions

6.4 Paired–Category Logit Modeling of Ordinal Responses

Exercises

7. Loglinear Models for Contingency Tables and Counts

7.1 Loglinear Models for Counts in Contingency Tables

7.2 Statistical Inference for Loglinear Models

7.3 The Loglinear Logistic Model Connection

7.4 Independence Graphs and Collapsibility

7.5 Modeling Ordinal Associations in Contingency Tables

7.6 Loglinear Modeling of Count Response Variables

Exercises

8. Models for Matched Pairs

8.1 Comparing Dependent Proportions for Binary Matched Pairs

8.2 Marginal Models and Subject–Specific Models for Matched Pairs

8.3 Comparing Proportions for Nominal Matched–Pairs Responses

8.4 Comparing Proportions for Ordinal Matched–Pairs Responses

8.5 Analyzing Rater Agreement

8.6 Bradley Terry Model for Paired Preferences

Exercises

9. Marginal Modeling of Correlated, Clustered Responses

9.1 Marginal Models Versus Subject–Specific Models

9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach

9.3 Marginal Modeling for Clustered Multinomial Responses

9.4 Transitional Modeling, Given the Past

9.5 Dealing with Missing Data

Exercises

10. Random Effects: Generalized Linear Mixed Models

10.1 Random Effects Modeling of Clustered Categorical Data

10.2 Examples: Random Effects Models for Binary Data

10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms

10.4 Multilevel (Hierarchical) Models

10.5 Latent Class Models

Exercises

11. Classification and Smoothing

11.1 Classification: Linear Discriminant Analysis

11.2 Classification: Tree–Based Prediction

11.3 Cluster Analysis for Categorical Responses

11.4 Smoothing: Generalized Additive Models

11.5 Regularization for High–Dimensional Categorical Data (Large p) Exercises

12. A Historical Tour of Categorical Data Analysis Appendix: Software for Categorical Data Analysis

A1: R for Categorical Data Analysis

A2: SAS for Categorical Data Analysis A3: Stata for Categorical Data Analysis A4: SPSS for Categorical Data Analysis

Brief Solutions to Some Odd–Numbered Exercises

Bibliography

Examples Index

Subject Index

O autorze

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).

Blurb

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.