Introduction to Categorical Data Analysis

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PROBLEMS 199 Table 6.16. Output on Modeling Happiness for Problem 6.7 Deviance and Pearson Goodness-of-Fit Statistics Criterion Value DF Value/DF Pr > ChiSq Deviance 3.2472 3 1.0824 0.3551 Pearson 3.2292 3 1.0764 0.3576 Testing Global Null Hypothesis: BETA = 0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 0.8876 1 0.3461 Wald 0.8976 1 0.3434 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 −3.2467 0.3404 90.9640
200 MULTICATEGORY LOGIT MODELS 6.9 A cumulative logit model is fitted to data from the 2004 General Social Survey, with Y = political ideology (extremely liberal or liberal, slightly liberal, moderate, slightly conservative, extremely conservative or conservative) and predictor religious preference (Protestant, Catholic, Jewish, None). With indicator variables for the first three religion categories, the ML fit has ˆα1 =−1.03, ˆα2 =−0.13, ˆα3 = 1.57, ˆα4 = 2.41, ˆβ1 =−1.27, ˆβ2 =−1.22, ˆβ3 =−0.44. a. Why are there four {ˆαj }?Whyis ˆα1 < ˆα2 < ˆα3 < ˆα4? b. Which group is estimated to be the (i) most liberal, (ii) most conservative? Why? c. Estimate the probability of the most liberal response for the Protestant and None groups. d. Use an estimated odds ratio to compare political ideology for the (i) Protestant and None groups, (ii) Protestant and Catholic groups. 6.10 Refer to the interpretations in Section 6.2.6 for the mental health data. Summarize the SES effect by finding P(Y ≤ 2) for high SES and for low SES, at the mean life events of 4.3. 6.11 Refer to Table 6.12. Treating job satisfaction as the response, analyze the data using a cumulative logit model. a. Describe the effect of income, using scores {3, 10, 20, 35}. b. Compare the estimated income effect to the estimate obtained after combining categories “Very dissatisfied” and “A little satisfied.” What property of the model does this reflect? c. Can you drop gender from the model in (a)? 6.12 Table 6.18 shows results from the 2000 General Social Survey relating happiness and religious attendance (1 = at most several times a year, 2 = once a month to several times a year, 3 = every week to several times a week). a. Fit a multinomial model. Conduct descriptive and inferential analyses about the association. b. Analyze the model goodness of fit. Table 6.18. GSS Data for Exercise 6.12 on Happiness Happiness Religion Not Too Happy Pretty Happy Very Happy 1 189 908 382 2 53 311 180 3 46 335 294
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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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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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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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