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Visualizing Categorical Data / Edition 1

Visualizing Categorical Data / Edition 1

by Michael Friendly

ISBN-10: 1580256600

ISBN-13: 9781580256605

Pub. Date: 02/06/2001

Publisher: SAS Publishing

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


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.

Product Details

SAS Publishing
Publication date:
Product dimensions:
8.30(w) x 10.82(h) x 0.73(d)

Table of Contents

How to Use This Bookx
Chapter 1Introduction1
1.1Data Visualization and Categorical Data1
1.2What Is Categorical Data?2
1.2.1Case Form vs. Frequency Form3
1.2.2Frequency Data vs. Count Data4
1.2.3Univariate, Bivariate, and Multivariate Data4
1.2.4Explanatory vs. Response Variables4
1.3Strategies for Categorical Data Analysis5
1.3.1Hypothesis-Testing Approaches5
1.3.2Model-Building Approaches6
1.4Graphical Methods for Categorical Data8
1.4.1Goals and Design Principles for Visual Data Display8
1.4.2Categorical Data Requires Different Graphical Methods11
1.5Visualization = Graphing + Fitting + Graphing13
1.5.1Static vs. Dynamic Graphics15
Chapter 2Fitting and Graphing Discrete Distributions17
2.2Discrete Distributions22
2.2.1The Binomial Distribution22
2.2.2The Poisson Distribution26
2.2.3The Negative Binomial Distribution29
2.2.4The Geometric Distribution31
2.2.5The Logarithmic Series Distribution32
2.2.6Power Series Family32
2.3Fitting Discrete Distributions33
2.3.1The GOODFIT Macro34
2.3.2Plots of Observed and Fitted Frequencies38
2.3.3The ROOTGRAM Macro40
2.3.4Maximum Likelihood Estimation42
2.3.5Fitting Discrete Distributions as Loglinear Models43
2.4Diagnosing Discrete Distributions: Ord Plots46
2.5Poissonness Plot49
2.5.1Features of the Poissonness Plot49
2.5.2Plot Construction49
2.5.3The POISPLOT Macro51
2.5.4Leverage and Influence53
2.5.5Plots for Other Distributions55
2.5.6DISTPLOT Macro55
2.6Chapter Summary56
Chapter 32-Way Contingency Tables59
3.2Tests of Association for 2-Way Tables62
3.2.1Notation and Terminology62
3.2.22 x 2 Tables63
3.2.3Larger Tables: Overall Analysis65
3.2.4Tests for Ordinal Variables67
3.2.5Sample CMH Profiles68
3.3Stratified Analysis70
3.3.1Assessing Homogeneity of Association73
3.4Fourfold Display for 2 x 2 Tables74
3.4.1Confidence Rings for Odds Ratio77
3.4.2The FOURFOLD Program78
3.4.3Stratified Analysis for 2 x 2 x k Tables79
3.5Sieve Diagrams85
3.5.1The SIEVE Program87
3.5.2Larger Tables88
3.6Association Plots90
3.7Observer Agreement91
3.7.1Measuring Agreement92
3.7.2Bangdiwala's Observer Agreement Chart94
3.7.3Observer Bias96
3.7.4The AGREE Program97
3.8Trilinear Plots97
3.9Chapter Summary102
Chapter 4Mosaic Displays for n-Way Tables105
4.22-Way Tables106
4.2.1Software for Mosaic Displays110
4.33-Way Tables116
4.3.1Fitting Models117
4.3.2Causal Models120
4.3.3Partial Association126
4.4Mosaic Matrices for Categorical Data129
4.4.1Conditional Mosaic Matrices133
4.5Showing the Structure of Log-linear Models134
4.5.1Mutual Independence134
4.5.2Joint Independence136
4.5.3Conditional Independence138
4.6Chapter Summary139
Chapter 5Correspondence Analysis141
5.2Simple Correspondence Analysis143
5.2.1Notation and Terminology143
5.2.2Geometric and Statistical Properties144
5.2.3The CORRESP Procedure145
5.2.4The CORRESP Macro149
5.2.5Quasi-Independence and Structural Zeros153
5.3Properties of Category Scores154
5.3.1Optimal Category Scores154
5.3.2Simultaneous Linear Regressions156
5.4Multi-Way Tables160
5.4.1Marginal Tables and Supplementary Variables164
5.5Multiple Correspondence Analysis165
5.5.1Bivariate MCA165
5.5.2The Burt Matrix169
5.5.3Multivariate MCA169
5.6Extended MCA: Showing Interactions in 2[superscript Q] Tables177
5.7Biplots for Contingency Tables188
5.7.1Biplots for 2-Way Tables188
5.7.2Biplots for 3-Way Tables191
5.8Chapter Summary193
Chapter 6Logistic Regression195
6.2The Logistic Regression Model196
6.2.1Plotting a Discrete Response: The LOGODDS Macro199
6.2.2Plotting a Discrete Response: Easy Smoothing with PROC GPLOT200
6.3Models for Quantitative Predictors202
6.3.1Fitting Logistic Regression Models202
6.3.2Plotting Predicted Probabilities204
6.4Logit Models for Qualitative Predictors212
6.4.1Plotting Results from PROC LOGISTIC215
6.5Multiple Logistic Regression Models217
6.5.1Models with Interaction223
6.5.2Effect Plots from Coefficients224
6.6Influence and Diagnostic Plots229
6.6.1Residuals and Leverage229
6.6.2Influence Diagnostics230
6.6.3Influence Output from PROC LOGISTIC231
6.6.4Diagnostic Plots of Influence Measures233
6.6.5Partial Residual and Added-Variable Plots237
6.7Polytomous Response Models240
6.7.1Ordinal Response: Proportional Odds Model241
6.7.2Plotting Results from PROC LOGISTIC242
6.7.3Nested Dichotomies245
6.7.4Generalized Logits250
6.8The Bradley-Terry-Luce Model for Paired Comparisons254
6.9Power and Sample Size for Logistic Regression259
6.9.1Binary Predictor: Comparing Two Proportions259
6.9.2Quantitative Predictor261
6.10Chapter Summary263
Chapter 7Log-linear and Logit Models265
7.2Log-linear Models for Counts266
7.2.1Log-linear Models as Discrete ANOVA Models267
7.2.2Log-linear Models as Discrete GLMs268
7.2.3Log-linear Models for 3-Way Tables269
7.3Fitting Log-linear Models269
7.3.1Goodness-of-Fit Tests270
7.3.3Using PROC CATMOD272
7.3.4Using PROC GENMOD273
7.3.5Using SAS/INSIGHT Software276
7.4Logit Models278
7.4.1Plotting Results for Logit Models280
7.4.2Zero Frequencies283
7.5Models for Ordinal Variables288
7.5.1Log-linear Models for Ordinal Variables289
7.5.2Adjacent Category Logit Models293
7.5.3Cumulative Logit Models296
7.6An Extended Example299
7.6.1A Fresh Look305
7.7Influence and Diagnostic Plots for Log-linear Models308
7.7.1Residuals and Diagnostics for Log-linear Models308
7.7.2Half-Normal Probability Plots of Residuals309
7.7.3Model Diagnostics with PROC GENMOD and the INFLGLIM Macro310
7.7.4Model Diagnostics with PROC CATMOD315
7.8Multivariate Responses317
7.8.1Examining Relations326
7.9Chapter Summary332
Appendix ASAS Programs and Macros335
A.1The ADDVAR Macro: Added Variable Plots for Logistic Regression337
A.2The AGREE Program: Observer Agreement Chart338
A.3The BIPLOT Macro: Generalized Biplots339
A.4The CATPLOT Macro: Plot Results from PROC CATMOD341
A.5The CORRESP Macro: Plotting PROC CORRESP Results343
A.6The DISTPLOT Macro: Plots for Discrete Distributions346
A.7The DUMMY Macro: Create Dummy Variables346
A.8The FOURFOLD Program: Fourfold Displays for 2 x 2 x k Tables348
A.9The GOODFIT Macro: Goodness-of-Fit for Discrete Distributions349
A.10The HALFNORM Macro: Half-Normal Plots for Generalized Linear Models350
A.11The INFLGLIM Macro: Influence Plots for Generalized Linear Models352
A.12The INFLOGIS Macro: Influence Plots for Logistic Regression Models354
A.13The INTERACT Macro: Create Interaction Variables355
A.14The LAGS Macro: Lagged Frequencies for Sequential Analysis355
A.15The LOGODDS Macro: Plot Empirical Logits for Binary Data358
A.16The MOSAICS Program: SAS/IML Modules for Mosaic Displays359
A.17The MOSAIC Macro: Mosaic Displays363
A.18The MOSMAT Macro: Mosaic Matrices365
A.19The ORDPLOT Macro: Ord Plot for Discrete Distributions366
A.20The PANELS Macro: Arrange Multiple Plots in Panels367
A.21The POISPLOT Macro: Poissonness Plot368
A.22The POWERLOG Macro: Power Analysis for Logistic Regression Table369
A.23The POWERRxC Macro: Power for 2-Way Frequency Tables370
A.24The POWER2x2 Macro: Power for 2 x 2 Frequency Tables371
A.25The ROBUST Macro: Robust Fitting for Linear Models373
A.26The ROOTGRAM Macro: Hanging Rootograms373
A.27The SIEVE Program: Sieve Diagrams374
A.28The SORT Macro: Sort a Dataset by the Value of a Statistic375
A.29The TABLE Macro: Construct a Grouped Frequency Table, with Recoding377
A.30The TRIPLOT Macro: Trilinear Plots for n x 3 Tables378
A.31Utility Macros379
A.31.1BARS: Create an Annotate Dataset to Draw Error Bars379
A.31.2EQUATE: Create AXIS Statements for a GPLOT with Equated Axes381
A.31.3GDISPLA: Device-Independent DISPLAY/NODISPLAY Control382
A.31.4GENSYM: Generate SYMBOL Statements for Multiple Curves382
A.31.5GSKIP: Device Independent Macro for Multiple Plots383
A.31.6LABEL: Label Points on a Plot385
A.31.7POINTS: Create an Annotate Dataset to Draw Points in a Plot386
A.31.8PSCALE: Construct an Annotate Dataset for a Probability Scale387
Appendix BDatasets389
B.1arthrit.sas: Arthritis Treatment Data390
B.2berkeley.sas: Berkeley Admissions Data391
B.3haireye.sas: Hair-color and Eye-color Data392
B.4icu.sas: ICU Data392
B.5lifeboat.sas: Lifeboats on the Titanic394
B.6marital.sas: Pre-marital Sex, Extra-marital Sex, and Divorce397
B.7mental.sas: Mental Impairment and Parents' SES397
B.8msdiag.sas: Diagnosis of Multiple Sclerosis398
B.9orings.sas: NASA Space Shuttle O-Ring Failures399
B.10suicide.sas: Suicide Rates in Germany399
B.11titanic.sas: Survival on the Titanic401
B.12vietnam.sas: Student Opinion about the Vietnam War402
B.13vision.sas: Visual Acuity in Left and Right Eyes403
B.14vonbort.sas: Deaths by Horse Kicks in the Prussian Army404
B.15vote.sas: Race and Politics in the 1980 U.S. Presidential Vote404
B.16wlfdata.sas: Women's Labor-force Participation405
Appendix CTables409
C.1CHI2TAB Program410
C.2x[superscript 2] Values411
C.3x[superscript 2]/df Values412
Author Index421
Example Index423
Subject Index427

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