Introduction to Categorical Data Analysis

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CHAPTER 10: RANDOM EFFECTS: GENERALIZED LINEAR MIXED MODELS 341 Table A.14. SAS Code for Marginal and Random Effects Modeling of Depression Data in Table 9.1 data depress; input case diagnose drug time outcome ©©; ∗ outcome=1 is normal; datalines; 1 0 0 0 1 1 0 0 1 1 1 0 0 2 1 ... 340 1 1 0 0 340 1 1 1 0 340 1 1 2 0 ; proc genmod descending; class case; model outcome = diagnose drug time drug∗time / dist=bin link=logit type3; repeated subject=case / type=exch corrw; proc nlmixed; eta = u + alpha + beta1∗diagnose + beta2∗drug + beta3∗time + beta4∗drug∗time; p = exp(eta)/(1 + exp(eta)); model outcome ˜ binary(p); random u ˜ normal(0, sigma∗sigma) subject = case; CHAPTER 10: RANDOM EFFECTS: GENERALIZED LINEAR MIXED MODELS PROC NLMIXED extends GLMs to GLMMs by including random effects. TableA.23 inAgresti (2002) shows how to fit the matched pairs model (10.3). TableA.15 analyzes the basketball data in Table 10.2. TableA.16 fits model (10.5) to Table 10.4 on abortion questions. This shows how to set the number of quadrature points for Gauss–Hermite quadrature (e.g., QPOINTS = ) and specify initial parameter values (perhaps based on an initial run with the default number of quadrature points). Table A.14 uses NLMIXED for the depression study of Table 9.1. Table A.22 in Agresti (2002) uses NLMIXED for ordinal modeling of the insomnia data in Table 9.6. Table A.15. SAS Code for GLMM Analyses of Basketball Data in Table 10.2 data basket; input player $ y n ©©; datalines; yao 10 13 frye 9 10 camby 10 15 okur 9 14 .... ; proc nlmixed; eta = alpha + u; p = exp(eta) / (1 + exp(eta)); model y ˜ binomial(n,p); random u ˜ normal(0,sigma∗sigma) subject=player; predict p out=new; proc print data=new;
342 APPENDIX A: SOFTWARE FOR CATEGORICAL DATA ANALYSIS Table A.16. SAS Code for GLMM Modelling of Opinion in Table 10.4 data new; input sex poor single any count; datalines; 1 1 1 1 342 ... 2 0 0 0 457 ; data new; set new; sex = sex-1; case = _n_; q1=1; q2=0; resp = poor; output; q1=0; q2=1; resp = single; output; q1=0; q2=0; resp = any; output; drop poor single any; proc nlmixed qpoints = 50; parms alpha=0 beta1=.8 beta2=.3 gamma=0 sigma=8.6; eta = u + alpha + beta1∗q1 + beta2∗q2 + gamma∗sex; p = exp(eta)/(1 + exp(eta)); model resp ˜ binary(p); ramdom u ˜ normal(0,sigma∗sigma) subject = case; replicate count;
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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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Page 311 and 312: 290 MODELING CORRELATED, CLUSTERED
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Page 365 and 366: Bibliography Agresti, A. (2002). Ca
Page 367 and 368: Index of Examples abortion, opinion
Page 369 and 370: 348 INDEX OF EXAMPLES lung cancer a
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
Page 377 and 378: 356 SUBJECT INDEX Residuals binomia
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Introduction to Categorical Data Analysis

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