Introduction to Categorical Data Analysis

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CHAPTER 10 371 CHAPTER 10 1. a. Using PROC NLMIXED in SAS, ( ˆβ,SE, ˆσ,SE) = (4.135, 0.713, 10.199, 1.792) for 1000 quadrature points. b. For given subject, estimated odds of belief in heaven are exp(4.135) = 62.5 times estimated odds of belief in hell. c. ˆβ = log(125/2) = 4.135 with SE = √ (1/125) + (1/2) = 0.713. 3. a. (i) 0.038, (ii) 0.020, (iii) 0.070. b. Sample size may be small in each county, and GLMM analysis borrows from whole. 5. a. 0.4, 0.8, 0.2, 0.6, 0.6, 1.0, 0.8, 0.4, 0.6, 0.2. b. logit(πi) = ui + α. ML estimates ˆα = 0.259 and ˆσ = 0.557. For average coin, estimated probability of head = 0.56. c. Using PROC NLMIXED in SAS, predicted values are 0.52, 0.63, 0.46, 0.57, 0.57, 0.68, 0.63, 0.52, 0.57, 0.46. 7. a. Strong associations between responses inflates GLMM estimates relative to marginal model estimates. b. Loglinear model focuses on strength of association between use of one substance and use of another, given whether or not one used remaining substance. The focus is not on the odds of having used one substance compared with the odds of using another. c. If ˆσ = 0, GLMM has the same fit as loglinear model (A, C, M), since conditional independence of responses given random effect translates to conditional independence marginally also. 9. For ˆβA = 0, ˆβB = 1.99 (SE = 0.35), ˆβC = 2.51 (SE = 0.37), with ˆσ = 0. 11. a. For given department, estimated odds of admission for female are exp(0.173) = 1.19 times estimated odds of admission for male. b. For given department, estimated odds of admission for female are exp(0.163) = 1.18 times estimated odds of admission for male. c. The estimated mean log odds ratio between gender and admissions, given department, is 0.176, corresponding to odds ratio = 1.19. Because of extra variance component, estimate of β is not as precise. d. Marginal odds ratio of exp(−0.07) = 0.93 in different direction, corresponding to odds of being admitted lower for females than males. 13. a. e 2.51 = 12.3, so estimated odds of response in category ≤ j (i.e., toward “always wrong” end of scale) on extramarital sex for a randomly selected
372 BRIEF SOLUTIONS TO SOME ODD-NUMBERED PROBLEMS subject are 12.3 times estimated odds of response in those categories for premarital sex for another randomly selected subject. b. Estimate of β much larger for GLMM, since a subject-specific estimate and variance component is large (recall Section 10.1.4). 17. a. At initial time, treatment effect = 0.058 (odds ratio = 1.06), so two groups have similar response distributions. At follow-up time, the treatment effect = 0.058 + 1.081 = 1.139 (odds ratio = 3.1). b. LR statistic =−2[−593.0 − (−621.0)] =56. Null distribution is equal mixture of degenerate at 0 and X 2 1 , and P -value is half that of X2 1 variate, and is 0 to many decimal places. 23. From Section 10.1.4, the effects in marginal models are smaller in absolute value than effects in GLMMs, with greater difference when ˆσ is larger. Here, the effect for GLMM is the same for each age group, but diminishes more for the older age group in the marginal model because the older age group has much larger ˆσ in GLMM.
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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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298 RANDOM EFFECTS: GENERALIZED LIN
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Page 365 and 366: Bibliography Agresti, A. (2002). Ca
Page 367 and 368: Index of Examples abortion, opinion
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Page 371 and 372: Subject Index Adjacent categories l
Page 373 and 374: 352 SUBJECT INDEX Exact inference (
Page 375 and 376: 354 SUBJECT INDEX Loglinear models
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Introduction to Categorical Data Analysis

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