Visualizing Categorical Data / Edition 1

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Overview

Visualizing Categorical Data, by Michael Friendly, offers many new and more easily accessible graphical methods for representing categorical data using SAS software. Graphical methods for quantitative data are well developed and widely used. However, until now with this comprehensive treatment, few graphical methods existed for categorical data. In this innovative book, Michael presents many aspects of the relationships among variables, the adequacy of a fitted model, and possibly unusual features of the data that can best be seen and appreciated in an informative graphical display. Filled with programs and datasets, this book focuses on the use, understanding, and interpretation of results. Where necessary, the statistical theory with a well-written explanation is also provided. Readers will also appreciate the implementation of these methods in general macros and programs that are described in the book. Michael Friendly, Ph.D., brings a tremendous amount of experience to the conceptualization, research, and writing of this invaluable text.
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Product Details

  • ISBN-13: 9781580256605
  • Publisher: SAS Publishing
  • Publication date: 2/6/2001
  • Edition number: 1
  • Pages: 438
  • Product dimensions: 8.30 (w) x 10.82 (h) x 0.73 (d)

Table of Contents

Preface ix
How to Use This Book x
Overview x
Acknowledgments xi
Chapter 1 Introduction 1
1.1 Data Visualization and Categorical Data 1
1.2 What Is Categorical Data? 2
1.2.1 Case Form vs. Frequency Form 3
1.2.2 Frequency Data vs. Count Data 4
1.2.3 Univariate, Bivariate, and Multivariate Data 4
1.2.4 Explanatory vs. Response Variables 4
1.3 Strategies for Categorical Data Analysis 5
1.3.1 Hypothesis-Testing Approaches 5
1.3.2 Model-Building Approaches 6
1.4 Graphical Methods for Categorical Data 8
1.4.1 Goals and Design Principles for Visual Data Display 8
1.4.2 Categorical Data Requires Different Graphical Methods 11
1.5 Visualization = Graphing + Fitting + Graphing 13
1.5.1 Static vs. Dynamic Graphics 15
Chapter 2 Fitting and Graphing Discrete Distributions 17
2.1 Introduction 17
2.2 Discrete Distributions 22
2.2.1 The Binomial Distribution 22
2.2.2 The Poisson Distribution 26
2.2.3 The Negative Binomial Distribution 29
2.2.4 The Geometric Distribution 31
2.2.5 The Logarithmic Series Distribution 32
2.2.6 Power Series Family 32
2.3 Fitting Discrete Distributions 33
2.3.1 The GOODFIT Macro 34
2.3.2 Plots of Observed and Fitted Frequencies 38
2.3.3 The ROOTGRAM Macro 40
2.3.4 Maximum Likelihood Estimation 42
2.3.5 Fitting Discrete Distributions as Loglinear Models 43
2.4 Diagnosing Discrete Distributions: Ord Plots 46
2.5 Poissonness Plot 49
2.5.1 Features of the Poissonness Plot 49
2.5.2 Plot Construction 49
2.5.3 The POISPLOT Macro 51
2.5.4 Leverage and Influence 53
2.5.5 Plots for Other Distributions 55
2.5.6 DISTPLOT Macro 55
2.6 Chapter Summary 56
Chapter 3 2-Way Contingency Tables 59
3.1 Introduction 59
3.2 Tests of Association for 2-Way Tables 62
3.2.1 Notation and Terminology 62
3.2.2 2 x 2 Tables 63
3.2.3 Larger Tables: Overall Analysis 65
3.2.4 Tests for Ordinal Variables 67
3.2.5 Sample CMH Profiles 68
3.3 Stratified Analysis 70
3.3.1 Assessing Homogeneity of Association 73
3.4 Fourfold Display for 2 x 2 Tables 74
3.4.1 Confidence Rings for Odds Ratio 77
3.4.2 The FOURFOLD Program 78
3.4.3 Stratified Analysis for 2 x 2 x k Tables 79
3.5 Sieve Diagrams 85
3.5.1 The SIEVE Program 87
3.5.2 Larger Tables 88
3.6 Association Plots 90
3.7 Observer Agreement 91
3.7.1 Measuring Agreement 92
3.7.2 Bangdiwala's Observer Agreement Chart 94
3.7.3 Observer Bias 96
3.7.4 The AGREE Program 97
3.8 Trilinear Plots 97
3.9 Chapter Summary 102
Chapter 4 Mosaic Displays for n-Way Tables 105
4.1 Introduction 105
4.2 2-Way Tables 106
4.2.1 Software for Mosaic Displays 110
4.3 3-Way Tables 116
4.3.1 Fitting Models 117
4.3.2 Causal Models 120
4.3.3 Partial Association 126
4.4 Mosaic Matrices for Categorical Data 129
4.4.1 Conditional Mosaic Matrices 133
4.5 Showing the Structure of Log-linear Models 134
4.5.1 Mutual Independence 134
4.5.2 Joint Independence 136
4.5.3 Conditional Independence 138
4.6 Chapter Summary 139
Chapter 5 Correspondence Analysis 141
5.1 Introduction 141
5.2 Simple Correspondence Analysis 143
5.2.1 Notation and Terminology 143
5.2.2 Geometric and Statistical Properties 144
5.2.3 The CORRESP Procedure 145
5.2.4 The CORRESP Macro 149
5.2.5 Quasi-Independence and Structural Zeros 153
5.3 Properties of Category Scores 154
5.3.1 Optimal Category Scores 154
5.3.2 Simultaneous Linear Regressions 156
5.4 Multi-Way Tables 160
5.4.1 Marginal Tables and Supplementary Variables 164
5.5 Multiple Correspondence Analysis 165
5.5.1 Bivariate MCA 165
5.5.2 The Burt Matrix 169
5.5.3 Multivariate MCA 169
5.6 Extended MCA: Showing Interactions in 2[superscript Q] Tables 177
5.7 Biplots for Contingency Tables 188
5.7.1 Biplots for 2-Way Tables 188
5.7.2 Biplots for 3-Way Tables 191
5.8 Chapter Summary 193
Chapter 6 Logistic Regression 195
6.1 Introduction 195
6.2 The Logistic Regression Model 196
6.2.1 Plotting a Discrete Response: The LOGODDS Macro 199
6.2.2 Plotting a Discrete Response: Easy Smoothing with PROC GPLOT 200
6.3 Models for Quantitative Predictors 202
6.3.1 Fitting Logistic Regression Models 202
6.3.2 Plotting Predicted Probabilities 204
6.4 Logit Models for Qualitative Predictors 212
6.4.1 Plotting Results from PROC LOGISTIC 215
6.5 Multiple Logistic Regression Models 217
6.5.1 Models with Interaction 223
6.5.2 Effect Plots from Coefficients 224
6.6 Influence and Diagnostic Plots 229
6.6.1 Residuals and Leverage 229
6.6.2 Influence Diagnostics 230
6.6.3 Influence Output from PROC LOGISTIC 231
6.6.4 Diagnostic Plots of Influence Measures 233
6.6.5 Partial Residual and Added-Variable Plots 237
6.7 Polytomous Response Models 240
6.7.1 Ordinal Response: Proportional Odds Model 241
6.7.2 Plotting Results from PROC LOGISTIC 242
6.7.3 Nested Dichotomies 245
6.7.4 Generalized Logits 250
6.8 The Bradley-Terry-Luce Model for Paired Comparisons 254
6.9 Power and Sample Size for Logistic Regression 259
6.9.1 Binary Predictor: Comparing Two Proportions 259
6.9.2 Quantitative Predictor 261
6.10 Chapter Summary 263
Chapter 7 Log-linear and Logit Models 265
7.1 Introduction 265
7.2 Log-linear Models for Counts 266
7.2.1 Log-linear Models as Discrete ANOVA Models 267
7.2.2 Log-linear Models as Discrete GLMs 268
7.2.3 Log-linear Models for 3-Way Tables 269
7.3 Fitting Log-linear Models 269
7.3.1 Goodness-of-Fit Tests 270
7.3.2 Software 272
7.3.3 Using PROC CATMOD 272
7.3.4 Using PROC GENMOD 273
7.3.5 Using SAS/INSIGHT Software 276
7.4 Logit Models 278
7.4.1 Plotting Results for Logit Models 280
7.4.2 Zero Frequencies 283
7.5 Models for Ordinal Variables 288
7.5.1 Log-linear Models for Ordinal Variables 289
7.5.2 Adjacent Category Logit Models 293
7.5.3 Cumulative Logit Models 296
7.6 An Extended Example 299
7.6.1 A Fresh Look 305
7.7 Influence and Diagnostic Plots for Log-linear Models 308
7.7.1 Residuals and Diagnostics for Log-linear Models 308
7.7.2 Half-Normal Probability Plots of Residuals 309
7.7.3 Model Diagnostics with PROC GENMOD and the INFLGLIM Macro 310
7.7.4 Model Diagnostics with PROC CATMOD 315
7.8 Multivariate Responses 317
7.8.1 Examining Relations 326
7.9 Chapter Summary 332
Appendix A SAS Programs and Macros 335
A.1 The ADDVAR Macro: Added Variable Plots for Logistic Regression 337
A.2 The AGREE Program: Observer Agreement Chart 338
A.3 The BIPLOT Macro: Generalized Biplots 339
A.4 The CATPLOT Macro: Plot Results from PROC CATMOD 341
A.5 The CORRESP Macro: Plotting PROC CORRESP Results 343
A.6 The DISTPLOT Macro: Plots for Discrete Distributions 346
A.7 The DUMMY Macro: Create Dummy Variables 346
A.8 The FOURFOLD Program: Fourfold Displays for 2 x 2 x k Tables 348
A.9 The GOODFIT Macro: Goodness-of-Fit for Discrete Distributions 349
A.10 The HALFNORM Macro: Half-Normal Plots for Generalized Linear Models 350
A.11 The INFLGLIM Macro: Influence Plots for Generalized Linear Models 352
A.12 The INFLOGIS Macro: Influence Plots for Logistic Regression Models 354
A.13 The INTERACT Macro: Create Interaction Variables 355
A.14 The LAGS Macro: Lagged Frequencies for Sequential Analysis 355
A.15 The LOGODDS Macro: Plot Empirical Logits for Binary Data 358
A.16 The MOSAICS Program: SAS/IML Modules for Mosaic Displays 359
A.17 The MOSAIC Macro: Mosaic Displays 363
A.18 The MOSMAT Macro: Mosaic Matrices 365
A.19 The ORDPLOT Macro: Ord Plot for Discrete Distributions 366
A.20 The PANELS Macro: Arrange Multiple Plots in Panels 367
A.21 The POISPLOT Macro: Poissonness Plot 368
A.22 The POWERLOG Macro: Power Analysis for Logistic Regression Table 369
A.23 The POWERRxC Macro: Power for 2-Way Frequency Tables 370
A.24 The POWER2x2 Macro: Power for 2 x 2 Frequency Tables 371
A.25 The ROBUST Macro: Robust Fitting for Linear Models 373
A.26 The ROOTGRAM Macro: Hanging Rootograms 373
A.27 The SIEVE Program: Sieve Diagrams 374
A.28 The SORT Macro: Sort a Dataset by the Value of a Statistic 375
A.29 The TABLE Macro: Construct a Grouped Frequency Table, with Recoding 377
A.30 The TRIPLOT Macro: Trilinear Plots for n x 3 Tables 378
A.31 Utility Macros 379
A.31.1 BARS: Create an Annotate Dataset to Draw Error Bars 379
A.31.2 EQUATE: Create AXIS Statements for a GPLOT with Equated Axes 381
A.31.3 GDISPLA: Device-Independent DISPLAY/NODISPLAY Control 382
A.31.4 GENSYM: Generate SYMBOL Statements for Multiple Curves 382
A.31.5 GSKIP: Device Independent Macro for Multiple Plots 383
A.31.6 LABEL: Label Points on a Plot 385
A.31.7 POINTS: Create an Annotate Dataset to Draw Points in a Plot 386
A.31.8 PSCALE: Construct an Annotate Dataset for a Probability Scale 387
Appendix B Datasets 389
B.1 arthrit.sas: Arthritis Treatment Data 390
B.2 berkeley.sas: Berkeley Admissions Data 391
B.3 haireye.sas: Hair-color and Eye-color Data 392
B.4 icu.sas: ICU Data 392
B.5 lifeboat.sas: Lifeboats on the Titanic 394
B.6 marital.sas: Pre-marital Sex, Extra-marital Sex, and Divorce 397
B.7 mental.sas: Mental Impairment and Parents' SES 397
B.8 msdiag.sas: Diagnosis of Multiple Sclerosis 398
B.9 orings.sas: NASA Space Shuttle O-Ring Failures 399
B.10 suicide.sas: Suicide Rates in Germany 399
B.11 titanic.sas: Survival on the Titanic 401
B.12 vietnam.sas: Student Opinion about the Vietnam War 402
B.13 vision.sas: Visual Acuity in Left and Right Eyes 403
B.14 vonbort.sas: Deaths by Horse Kicks in the Prussian Army 404
B.15 vote.sas: Race and Politics in the 1980 U.S. Presidential Vote 404
B.16 wlfdata.sas: Women's Labor-force Participation 405
Appendix C Tables 409
C.1 CHI2TAB Program 410
C.2 x[superscript 2] Values 411
C.3 x[superscript 2]/df Values 412
References 413
Author Index 421
Example Index 423
Subject Index 427
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