Introduction to Categorical Data Analysis

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PROBLEMS 235 7.5 Refer to Table 2.10 on death penalty verdicts. Let D = defendant’s race, V = victim’s race, and P = death penalty verdict. Table 7.20 shows output for fitting model (DV, DP, PV ). Estimates equal 0 at the second category for any variable. a. Report the estimated conditional odds ratio between D and P at each level of V . Interpret. b. The marginal odds ratio between D and P is 1.45. Contrast this odds ratio with that in (a), and remark on how Simpson’s paradox occurs for these data. c. Test the goodness of fit of this model. Interpret. d. Specify the corresponding logistic model with P as the response. Table 7.20. Computer Output for Problem 7.5 on Death Penalty Criteria For Assessing Goodness Of Fit Criterion DF Value Deviance 1 0.3798 Pearson Chi-Square 1 0.1978 Standard LR 95% Confidence Parameter DF Estimate Error Limits Intercept 1 3.9668 0.1374 3.6850 4.2245 v black 1 −5.6696 0.6459 −7.0608 −4.4854 d black 1 −1.5525 0.3262 −2.2399 −0.9504 p no 1 2.0595 0.1458 1.7836 2.3565 v*d black black 1 4.5950 0.3135 4.0080 5.2421 v*p black no 1 2.4044 0.6006 1.3068 3.7175 d*p black no 1 −0.8678 0.3671 −1.5633 −0.1140 LR Statistics Source DF Chi-Square Pr > ChiSq v*d 1 384.05
236 LOGLINEAR MODELS FOR CONTINGENCY TABLES Table 7.21. Data on Four Scales of the Myers–Briggs Personality Test Extroversion/Introversion E I Sensing/iNtuitive S N S N Thinking/Feeling Judging/Perceiving T F T F T F T F J 77 106 23 31 140 138 13 31 P 42 79 18 80 52 106 35 79 Source: Reproduced with special permission of CPP, Inc., Mountain View, CA 94043. Copyright 1996 by CPP, Inc. All rights reserved. Further reproduction is prohibited without the Publisher’s written consent. b. Fit the loglinear model of homogeneous association. Based on the fit, show that the estimated conditional association is strongest between the S/N and J/P scales. c. Using the model in (b), show that there is not strong evidence of conditional association between the E/I and T/F scale or between the E/I and J/P scales. 7.7 Refer to the previous exercise. Table 7.22 shows the fit of the model that assumes conditional independence between E/I and T/F and between E/I and J/P but has the other pairwise associations. a. Compare this to the fit of the model containing all the pairwise associations, which has deviance 10.16 with df = 5. What do you conclude? b. Show how to use the limits reported to construct a 95% likelihood-ratio confidence interval for the conditional odds ratio between the S/N and J/P scales. Interpret. Table 7.22. Partial Output for Fitting Loglinear Model to Table 7.21 Criteria For Assessing Goodness Of Fit Criterion DF Value Deviance 7 12.3687 Pearson Chi-Square 7 12.1996 Analysis Of Parameter Estimates Standard LR 95% confidence Wald Chi- Parameter DF Estimate Error limits Square EI*SN e n 1 0.3219 0.1360 0.0553 0.5886 5.60 SN*TF n f 1 0.4237 0.1520 0.1278 0.7242 7.77 SN*JP n j 1 −1.2202 0.1451 −1.5075 −0.9382 70.69 TF*JP f j 1 −0.5585 0.1350 −0.8242 −0.2948 17.12
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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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286 MODELING CORRELATED, CLUSTERED
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298 RANDOM EFFECTS: GENERALIZED LIN
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326 A HISTORICAL TOUR OF CATEGORICA
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Appendix A: Software for Categorica
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334 APPENDIX A: SOFTWARE FOR CATEGO
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Bibliography Agresti, A. (2002). Ca
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Index of Examples abortion, opinion
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348 INDEX OF EXAMPLES lung cancer a
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Subject Index Adjacent categories l
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352 SUBJECT INDEX Exact inference (
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354 SUBJECT INDEX Loglinear models
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356 SUBJECT INDEX Residuals binomia
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358 BRIEF SOLUTIONS TO SOME ODD-NUM
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Introduction to Categorical Data Analysis

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