Introduction to Categorical Data Analysis

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PROBLEMS 97 ML estimate ˆβ =−0.0337 has SE = 0.0130. Conduct the Wald test of H0: β = 0 against Ha: β �= 0. c. The likelihood-ratio 95% confidence interval for β is (−0.060, −0.008). Find the interval for the multiplicative annual effect on the accident rate, and interpret. 3.20 Table 3.9, based on a study with British doctors conducted by R. Doll and A. Bradford Hill, was analyzed by N. R. Breslow in A Celebration of Statistics, Berlin: Springer, 1985. a. For each age, compute the sample coronary death rates per 1000 person-years, for nonsmokers and smokers. To compare them, take their ratio and describe its dependence on age. b. Specify a main-effects Poisson model for the log rates having four parameters for age and one for smoking. Explain why this model assumes a constant ratio of nonsmokers’ to smokers’ coronary death rates over levels of age. Based on (a), would you expect this model to be appropriate? c. Based on (a), explain why it is sensible to add a quantitative interaction of age and smoking. Specify this model, and show that the log of the ratio of coronary death rates changes linearly with age. d. Fit the model in (b). Assign scores to the levels of age for a product interaction term between age and smoking, and fit the model in (c). Compare the fits by comparing the deviances. Interpret. Table 3.9. Data for Problem 3.20 Person-Years Coronary Deaths Age Nonsmokers Smokers Nonsmokers Smokers 35–44 18,793 52,407 2 32 45–54 10,673 43,248 12 104 55–64 5710 28,612 28 206 65–74 2585 12,663 28 186 75–84 1462 5317 31 102 Source: R. Doll and A. B. Hill, Natl Cancer Inst. Monogr., 19: 205–268, 1966. 3.21 For rate data, a GLM with identity link is μ/t = α + βx Explain why you could fit this model using t and tx as explanatory variables and with no intercept or offset terms.
98 GENERALIZED LINEAR MODELS 3.22 True, or false? a. An ordinary regression (or ANOVA) model that treats the response Y as normally distributed is a special case of a GLM, with normal random component and identity link function. b. With a GLM, Y does not need to have a normal distribution and one can model a function of the mean of Y instead of just the mean itself, but in order to get ML estimates the variance of Y must be constant at all values of predictors. c. The Pearson residual ei = (yi −ˆμi)/ √ ˆμi for a GLM has a large-sample standard normal distribution.
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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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Page 121 and 122: 100 LOGISTIC REGRESSION The logisti
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148 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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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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