Introduction to Categorical Data Analysis

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CHAPTER 2: CONTINGENCY TABLES 333 options, and exact conditional inference. PROC NLMIXED fits generalized linear mixed models (models with random effects). The examples below show SAS code (version 9), organized by chapter of presentation. For convenience, some of the examples enter data in the form of the contingency table displayed in the text. In practice, one would usually enter data at the subject level. Most of these tables and the full data sets are available at www.stat.ufl.edu/∼aa/cda/software.html. For more detailed discussion of the use of SAS for categorical data analyses, see specialized SAS publications such as Allison (1999) and Stokes et al. (2000). For application of SAS to clustered data, see Molenberghs and Verbeke (2005). CHAPTER 2: CONTINGENCY TABLES Table A.1 uses SAS to analyze Table 2.5. The @@ symbol indicates that each line of data contains more than one observation. Input of a variable as characters rather than numbers requires an accompanying $ label in the INPUT statement. Table A.1. SAS Code for Chi-Squared, Measures of Association, and Residuals with Party ID Data in Table 2.5 data table; input gender $ party $ count ©©; datalines; female dem 762 female indep 327 female repub 468 male dem 484 male inidep 239 male repub 477 ; proc freq order=data; weight count; tables gender∗party / chisq expected measures cmh1; proc genmod order=data; class gender party; model count = gender party / dist=poi link=log residuals; PROC FREQ forms the table with the TABLES statement, ordering row and column categories alphanumerically. To use instead the order in which the categories appear in the data set (e.g., to treat the variable properly in an ordinal analysis), use the ORDER=DATA option in the PROC statement. The WEIGHT statement is needed when one enters the contingency table instead of subject-level data. PROC FREQ can conduct chi-squared tests of independence (CHISQ option), show its estimated expected frequencies (EXPECTED), provide a wide assortment of measures of association and their standard errors (MEASURES), and provide ordinal statistic (2.10) with a “nonzero correlation” test (CMH1). One can also perform chi-squared tests using PROC GENMOD (using loglinear models discussed in the Chapter 7 section of this Appendix), as shown. Its RESIDUALS option provides cell residuals. The output labeled “StReschi” is the standardized residual (2.9). Table A.2 analyzes Table 2.8 on tasting tea. With PROC FREQ, for 2 × 2 tables the MEASURES option in the TABLES statement provides confidence intervals for the
334 APPENDIX A: SOFTWARE FOR CATEGORICAL DATA ANALYSIS Table A.2. SAS Code for Fisher’s Exact Test and Confidence Intervals for Odds Ratio for Tea-Tasting Data in Table 2.8 data fisher; input poured guess count ©©; datalines; 1 1 3 1 2 1 2 1 1 2 2 3 ; proc freq; weight count; tables poured*guess / measures riskdiff; exact fisher or / alpha=.05; odds ratio (labeled “case-control” on output) and the relative risk, and the RISKDIFF option provides intervals for the proportions and their difference. For tables having small cell counts, the EXACT statement can provide various exact analyses. These include Fisher’s exact test and its generalization for I × J tables, treating variables as nominal, with keyword FISHER. The OR keyword gives the odds ratio and its largesample and small-sample confidence intervals. Other EXACT statement keywords include binomial tests for 1 × 2 tables (keyword BINOMIAL), exact trend tests for I × 2 tables (TREND), and exact chi-squared tests (CHISQ) and exact correlation tests for I × J tables (MHCHI). CHAPTER 3: GENERALIZED LINEAR MODELS PROC GENMOD fits GLMs. It specifies the response distribution in the DIST option (“poi” for Poisson, “bin” for binomial, “mult” for multinomial, “negbin” for negative binomial) and specifies the link in the LINK option. Table A.3 illustrates for binary regression models for the snoring and heart attack data of Table 3.1. For binomial grouped data, the response in the model statements takes the form of the number of “successes” divided by the number of cases. Table A.4 fits Poisson and negative binomial loglinear models for the horseshoe crab data of Table 3.2. Table A.3. SAS Code for Binary GLMs for Snoring Data in Table 3.1 data glm; input snoring disease total ©©; datalines; 0 24 1379 2 35 638 4 21 213 5 30 254 ; proc genmod; model disease/total = snoring / dist=bin link=identity; proc genmod; model disease/total = snoring / dist=bin link=logit; PROC GAM fits generalized additive models. These can smooth data, as illustrated by Figure 3.5.
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www.dbeBooks.com - An Ebook Library
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An Introduction to Categorical Data
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Copyright © 2007 by John Wiley & S
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vi CONTENTS 2.1.3 Sensitivity and S
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viii CONTENTS 4.1.5 Logistic Regres
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x CONTENTS 6.3.1 Adjacent-Categorie
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xii CONTENTS 9. Modeling Correlated
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Preface to the Second Edition In re
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PREFACE TO THE SECOND EDITION xvii
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2 INTRODUCTION sciences (e.g., cate
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4 INTRODUCTION models for continuou
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6 INTRODUCTION The multinomial is a
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8 INTRODUCTION precise, in terms of
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10 INTRODUCTION that are judged pla
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12 INTRODUCTION In this text, we us
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14 INTRODUCTION 1.4.4 Small-Sample
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16 INTRODUCTION For small samples,
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18 INTRODUCTION the outcome y equal
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20 INTRODUCTION a. Calculate the lo
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22 CONTINGENCY TABLES Suppose there
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24 CONTINGENCY TABLES Figure 2.1. T
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26 CONTINGENCY TABLES compare two g
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28 CONTINGENCY TABLES It can be any
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30 CONTINGENCY TABLES The sample od
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32 CONTINGENCY TABLES For Table 2.3
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34 CONTINGENCY TABLES the binomial
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36 CONTINGENCY TABLES The df value
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38 CONTINGENCY TABLES Table 2.5. Cr
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40 CONTINGENCY TABLES that combines
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42 CONTINGENCY TABLES Large values
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44 CONTINGENCY TABLES when the data
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46 CONTINGENCY TABLES n11 equals P(
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48 CONTINGENCY TABLES the observed
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50 CONTINGENCY TABLES Table 2.10. D
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52 CONTINGENCY TABLES Figure 2.4. P
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54 CONTINGENCY TABLES marginal tabl
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56 CONTINGENCY TABLES 2.4 A newspap
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58 CONTINGENCY TABLES a. Construct
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60 CONTINGENCY TABLES Table 2.14. D
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62 CONTINGENCY TABLES a. Show that
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64 CONTINGENCY TABLES 2.36 Give a
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66 GENERALIZED LINEAR MODELS 3.1 CO
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68 GENERALIZED LINEAR MODELS The ne
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70 GENERALIZED LINEAR MODELS Figure
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72 GENERALIZED LINEAR MODELS fitted
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74 GENERALIZED LINEAR MODELS 3.3 GE
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76 Table 3.2. Number of Crab Satell
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82 GENERALIZED LINEAR MODELS with S
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84 GENERALIZED LINEAR MODELS Simila
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86 GENERALIZED LINEAR MODELS provid
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88 GENERALIZED LINEAR MODELS 3.5 FI
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90 GENERALIZED LINEAR MODELS Table
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92 GENERALIZED LINEAR MODELS 37 obs
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94 GENERALIZED LINEAR MODELS Table
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96 GENERALIZED LINEAR MODELS 3.18 T
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98 GENERALIZED LINEAR MODELS 3.22 T
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100 LOGISTIC REGRESSION The logisti
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102 LOGISTIC REGRESSION of observat
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104 LOGISTIC REGRESSION for crabs i
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106 LOGISTIC REGRESSION that P(Y =
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108 LOGISTIC REGRESSION −2(L0 −
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110 LOGISTIC REGRESSION The estimat
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112 LOGISTIC REGRESSION Table 4.4.
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114 LOGISTIC REGRESSION 4.3.4 The C
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116 LOGISTIC REGRESSION 4.4.1 Examp
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118 LOGISTIC REGRESSION 4.4.2 Model
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120 LOGISTIC REGRESSION 1.2, based
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122 LOGISTIC REGRESSION activity of
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128 LOGISTIC REGRESSION 0 = no) and
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132 LOGISTIC REGRESSION b. In Table
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136 LOGISTIC REGRESSION c. The lack
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138 BUILDING AND APPLYING LOGISTIC
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174 MULTICATEGORY LOGIT MODELS are
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176 MULTICATEGORY LOGIT MODELS By e
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178 MULTICATEGORY LOGIT MODELS 6.1.
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180 MULTICATEGORY LOGIT MODELS 6.2
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182 MULTICATEGORY LOGIT MODELS Then
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184 MULTICATEGORY LOGIT MODELS Like
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186 MULTICATEGORY LOGIT MODELS Tabl
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188 MULTICATEGORY LOGIT MODELS only
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190 MULTICATEGORY LOGIT MODELS 6.3.
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194 MULTICATEGORY LOGIT MODELS With
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196 MULTICATEGORY LOGIT MODELS high
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CHAPTER 7 Loglinear Models for Cont
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206 LOGLINEAR MODELS FOR CONTINGENC
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216 Table 7.9. Injury (I) by Gender
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CHAPTER 8 Models for Matched Pairs
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246 MODELS FOR MATCHED PAIRS are nu
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248 MODELS FOR MATCHED PAIRS An alt
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250 MODELS FOR MATCHED PAIRS This c
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252 MODELS FOR MATCHED PAIRS only a
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254 MODELS FOR MATCHED PAIRS Table
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258 MODELS FOR MATCHED PAIRS from t
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260 MODELS FOR MATCHED PAIRS likeli
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262 MODELS FOR MATCHED PAIRS the ad
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264 MODELS FOR MATCHED PAIRS 8.5.5
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266 MODELS FOR MATCHED PAIRS ˆβ4
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268 MODELS FOR MATCHED PAIRS 8.7 Re
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270 MODELS FOR MATCHED PAIRS b. The
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CHAPTER 9 Modeling Correlated, Clus
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278 MODELING CORRELATED, CLUSTERED
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280 MODELING CORRELATED, CLUSTERED
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Page 375 and 376: 354 SUBJECT INDEX Loglinear models
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Introduction to Categorical Data Analysis

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