Categorical data analysis by example / Graham J. G. Upton.

Format:

Book

Author/Creator:

Upton, Graham J. G., author.

Series:

New York Academy of Sciences Ser.

Language:

English

Subjects (All):

Log-linear models.

Multivariate analysis.

Physical Description:

1 online resource (215 pages) : illustrations, tables, graphs

Place of Publication:

Hoboken, New Jersey : Wiley, 2017.

Summary:

Introduces the key concepts in the analysis of categoricaldata with illustrative examples and accompanying R code This book is aimed at all those who wish to discover how to analyze categorical data without getting immersed in complicated mathematics and without needing to wade through a large amount of prose. It is aimed at researchers with their own data ready to be analyzed and at students who would like an approachable alternative view of the subject. Each new topic in categorical data analysis is illustrated with an example that readers can apply to their own sets of data. In many cases, R code is given and excerpts from the resulting output are presented. In the context of log-linear models for cross-tabulations, two specialties of the house have been included: the use of cobweb diagrams to get visual information concerning significant interactions, and a procedure for detecting outlier category combinations. The R code used for these is available and may be freely adapted. In addition, this book: Uses an example to illustrate each new topic in categorical data Provides a clear explanation of an important subject Is understandable to most readers with minimal statistical and mathematical backgrounds Contains examples that are accompanied by R code and resulting output Includes starred sections that provide more background details for interested readers Categorical Data Analysis by Example is a reference for students in statistics and researchers in other disciplines, especially the social sciences, who use categorical data. This book is also a reference for practitioners in market research, medicine, and other fields. GRAHAM J. G. UPTON is formerly Professor of Applied Statistics, Department of Mathematical Sciences, University of Essex. Dr. Upton is author of The Analysis of Cross-tabulated Data (1978) and joint author of Spatial Data Analysis by Example (2 volumes, 1995), both published by Wiley. He is the lead author of The Oxford Dictionary of Statistics (OUP, 2014). His books have been translated into Japanese, Russian, and Welsh. "

Contents:

Intro

CATEGORICAL DATA ANALYSIS BY EXAMPLE

Contents

Preface

Acknowledgments

1 Introduction

1.1 What are Categorical Data?

1.2 A Typical Data Set

1.3 Visualization and Cross-Tabulation

1.4 Samples, Populations, and Random Variation

1.5 Proportion, Probability, and Conditional Probability

1.6 Probability Distributions

1.6.1 The Binomial Distribution

1.6.2 The Multinomial Distribution

1.6.3 The Poisson Distribution

1.6.4 The Normal Distribution

1.6.5 The Chi-Squared ( 2) Distribution

1.7 *The Likelihood

2 Estimation and Inference for Categorical Data

2.1 Goodness of Fit

2.1.1 Pearson's X2 Goodness-of-Fit Statistic

2.1.2 *The Link between X2 and the Poisson and 2-Distributions

2.1.3 The Likelihood-Ratio Goodness-of-Fit Statistic, G2

2.1.4 *Why the G2 and X2 Statistics Usually have Similar Values

2.2 Hypothesis Tests for a Binomial Proportion (Large Sample)

2.2.1 The Normal Score Test

2.2.2 *Link to Pearson's X2 Goodness-of-Fit Test

2.2.3 G2 for a Binomial Proportion

2.3 Hypothesis Tests for a Binomial Proportion (Small Sample)

2.3.1 One-Tailed Hypothesis Test

2.3.2 Two-Tailed Hypothesis Tests

2.4 Interval Estimates for a Binomial Proportion

2.4.1 Laplace's Method

2.4.2 Wilson's Method

2.4.3 The Agresti-Coull Method

2.4.4 Small Samples and Exact Calculations

References

3 The 2 × 2 Contingency Table

3.1 Introduction

3.2 Fisher's Exact Test (for Independence)

3.2.1 *Derivation of the Exact Test Formula

3.3 Testing Independence with Large Cell Frequencies

3.3.1 Using Pearson's Goodness-of-Fit Test

3.3.2 The Yates Correction

3.4 The 2 × 2 Table in a Medical Context

3.5 Measuring Lack of Independence (Comparing Proportions)

3.5.1 Difference of Proportions

3.5.2 Relative Risk

3.5.3 Odds-Ratio

References.

4 The I × J Contingency Table

4.1 Notation

4.2 Independence in the I × J Contingency Table

4.2.1 Estimation and Degrees of Freedom

4.2.2 Odds-Ratios and Independence

4.2.3 Goodness of Fit and Lack of Fit of the Independence Model

4.3 Partitioning

4.3.1 *Additivity of G2

4.3.2 Rules for Partitioning

4.4 Graphical Displays

4.4.1 Mosaic Plots

4.4.2 Cobweb Diagrams

4.5 Testing Independence with Ordinal Variables

5 The Exponential Family

5.1 Introduction

5.2 The Exponential Family

5.2.1 The Exponential Dispersion Family

5.3 Components of a General Linear Model

5.4 Estimation

6 A Model Taxonomy

6.1 Underlying Questions

6.1.1 Which Variables are of Interest?

6.1.2 What Categories should be Used?

6.1.3 What is the Type of Each Variable?

6.1.4 What is the Nature of Each Variable?

6.2 Identifying the Type of Model

7 The 2 × J Contingency Table

7.1 A Problem with X2 (and G2)

7.2 Using the Logit

7.2.1 Estimation of the Logit

7.2.2 The Null Model

7.3 Individual Data and Grouped Data

7.4 Precision, Confidence Intervals, and Prediction Intervals

7.4.1 Prediction Intervals

7.5 Logistic Regression with a Categorical Explanatory Variable

7.5.1 Parameter Estimates with Categorical Variables (J &gt

2)

7.5.2 The Dummy Variable Representation of a Categorical Variable

8 Logistic Regression with Several Explanatory Variables

8.1 Degrees of Freedom when there are no Interactions

8.2 Getting a Feel for the Data

8.3 Models with two-Variable Interactions

8.3.1 Link to the Testing of Independence between Two Variables

9 Model Selection and Diagnostics

9.1 Introduction

9.1.1 Ockham's Razor

9.2 Notation for Interactions and for Models

9.3 Stepwise Methods for Model Selection Using G2.

9.3.1 Forward Selection

9.3.2 Backward Elimination

9.3.3 Complete Stepwise

9.4 AIC and Related Measures

9.5 The Problem Caused by Rare Combinations of Events

9.5.1 Tackling the Problem

9.6 Simplicity Versus Accuracy

9.7 DFBETAS

10 Multinomial Logistic Regression

10.1 A Single Continuous Explanatory Variable

10.2 Nominal Categorical Explanatory Variables

10.3 Models for an Ordinal Response Variable

10.3.1 Cumulative Logits

10.3.2 Proportional Odds Models

10.3.3 Adjacent-Category Logit Models

10.3.4 Continuation-Ratio Logit Models

11 Log-Linear Models for I × J Tables

11.1 The Saturated Model

11.1.1 Cornered Constraints

11.1.2 Centered Constraints

11.2 The Independence Model for an I × J Table

12 Log-Linear Models for I × J × K Tables

12.1 Mutual Independence: A∕B∕C

12.2 The Model AB∕C

12.3 Conditional Independence and Independence

12.4 The Model AB∕AC

12.5 The Models AB∕AC∕BC and ABC

12.6 Simpson's Paradox

12.7 Connection between Log-Linear Models and Logistic Regression

Reference

13 Implications and Uses of Birch's Result

13.1 Birch's Result

13.2 Iterative Scaling

13.3 The Hierarchy Constraint

13.4 Inclusion of the All-Factor Interaction

13.5 Mostellerizing

14 Model Selection for Log-Linear Models

14.1 Three Variables

14.2 More than Three Variables

15 Incomplete Tables, Dummy Variables, and Outliers

15.1 Incomplete Tables

15.1.1 Degrees of Freedom

15.2 Quasi-independence

15.3 Dummy Variables

15.4 Detection of Outliers

16 Panel Data and Repeated Measures

16.1 The Mover-Stayer Model

16.2 The Loyalty Model

16.3 Symmetry

16.4 Quasi-Symmetry

16.5 The Loyalty-Distance Model

Appendix R Code for Cobweb Function

Index

Author Index.

Index of Examples

EULA.

Notes:

Includes index.

Includes bibliographical references at the end of each chapters and indexes.

Description based on print version record.

ISBN:

1-119-30793-7

1-119-45038-1

OCLC:

959667473