an introduction to generalized linear models - GDM@FUDAN ...

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AN INTRODUCTION TO GENERALIZED LINEAR MODELS SECOND EDITION Annette J. Dobson CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C.
Page 1: CHAPMAN & HALL/CRC Texts in Statist
Page 5 and 6: Preface Contents 1 Introduction 1.1
Page 7 and 8: 10 Survival Analysis 10.1 Introduct
Page 9 and 10: 1 Introduction 1.1 Background This
Page 11 and 12: Table 1.1 Major methods of statisti
Page 13 and 14: ofgeneralized linear models althoug
Page 15 and 16: 3. Let Y1, ..., Yn denote Normally
Page 17 and 18: divided by its degrees offreedom, F
Page 19 and 20: l(θ; y) = log L(θ; y), since the
Page 21 and 22: (i.e., the matrix ofsecond derivati
Page 23 and 24: Table 1.3 Successive approximations
Page 25 and 26: 2 Model Fitting 2.1 Introduction Th
Page 27 and 28: IfH1is true, then the log-likelihoo
Page 29 and 30: estimated in order to calculate to
Page 31 and 32: where xjk is the gestational age of
Page 33 and 34: Table 2.4 Summary of data on birthw
Page 35 and 36: Residuals Residuals Percent 2 1 0 -
Page 37 and 38: sampling distributions ofthe corres
Page 39 and 40: is categorical how many categories
Page 41 and 42: Cox and Snell, 1968; Prigibon, 1981
Page 43 and 44: 2.4Notation and coding for explanat
Page 45 and 46: and the rows of X are as follows Gr
Page 47 and 48: (a) Conduct an exploratory analysis
Page 49 and 50: (d) List the assumptions made for (
Page 51 and 52: putation involving numerical optimi
Page 53 and 54:
worthwhile trying to identify a tra
Page 55 and 56:
We also need expressions for the ex
Page 57 and 58:
1. Response variables Y1,... ,YN wh
Page 59 and 60:
Table 3.2 Numbers of deaths from co
Page 61 and 62:
3.4 Use results (3.9) and (3.12) to
Page 63 and 64:
4 Estimation 4.1 Introduction This
Page 65 and 66:
x (m - 1) x (m) Figure 4.3 Newton-R
Page 67 and 68:
Table 4.2 Details of Newton-Raphson
Page 69 and 70:
y differentiating (4.13) and substi
Page 71 and 72:
Table 4.3 Data for Poisson regressi
Page 73 and 74:
Table 4.4 Successive approximations
Page 75 and 76:
5 Inference 5.1 Introduction The tw
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consistent with the general result
Page 79 and 80:
approximated by its expected value
Page 81 and 82:
Hence E � (b − β)(b − β) T
Page 83 and 84:
For Yi’s with other distributions
Page 85 and 86:
8, D has a chi-squared distribution
Page 87 and 88:
Consider the null hypothesis ⎡
Page 89 and 90:
(a) Find the Wald statistic (�π
Page 91 and 92:
6.2.2 Least squares estimation IfE(
Page 93 and 94:
Table 6.2 Multiple hypothesis tests
Page 95 and 96:
the minimum value ofthe sum ofsquar
Page 97 and 98:
and ⎡ X T ⎢ X = ⎢ ⎣ 20 923
Page 99 and 100:
or ‘worst possible’ value of S.
Page 101 and 102:
Table 6.6 Dried weights yi of plant
Page 103 and 104:
The first row (or column) ofthe (J
Page 105 and 106:
so For the plant weight data and Y
Page 107 and 108:
4. The model formed by omitting eff
Page 109 and 110:
Finally for the model with only a m
Page 111 and 112:
6.5 Analysis of covariance Analysis
Page 113 and 114:
For the reduced model (6.14) �
Page 115 and 116:
6.7 Exercises 6.1 Table 6.15 shows
Page 117 and 118:
Table 6.17 Cholesterol (CHOL), age
Page 119 and 120:
6.8 Table 6.20 shows the data from
Page 121 and 122:
Table 7.1 Frequencies for N binomia
Page 123 and 124:
x x Figure 7.2 Normal distribution:
Page 125 and 126:
and log(1 − πi) =− log [1 + ex
Page 127 and 128:
Table 7.4 Comparison of observed nu
Page 129 and 130:
Proportion germinated 0.7 0.6 0.5 4
Page 131 and 132:
which is asymptotically equivalent
Page 133 and 134:
From equation (7.5), �m residuals
Page 135 and 136:
Proportion with symptoms of senilit
Page 137 and 138:
Table 7.10 Hosmer-Lemeshow test for
Page 139 and 140:
(a) Are the proportions of graduate
Page 141 and 142:
category 2, and so on, then let ⎡
Page 143 and 144:
(iii) Likelihood ratio chi-squared
Page 145 and 146:
Women: preference for air condition
Page 147 and 148:
Table 8.3 Results from fitting the
Page 149 and 150:
π 1 π 2 π 3 π 4 C1 C2 C3 Figure
Page 151 and 152:
The adjacent category logit model i
Page 153 and 154:
Table 8.4 Results of proportional o
Page 155 and 156:
(c) Use a Wald statistic to test th
Page 157 and 158:
variables. The study design may mea
Page 159 and 160:
series expansion given in Section 7
Page 161 and 162:
for smokers and zero for non-smoker
Page 163 and 164:
column totals. It appears that Hutc
Page 165 and 166:
similar to the ulcer patients with
Page 167 and 168:
� k θ.k =1. This hypothesis can
Page 169 and 170:
9.6 Inference for log-linear models
Page 171 and 172:
Table 9.10 Log-linear models for th
Page 173 and 174:
9.9 Exercises 9.1 Let Y1, ..., YN b
Page 175 and 176:
Table 9.14 Contingency table with 2
Page 177 and 178:
1 2 D 3 A D 4 L 5 D D TO TL TC time
Page 179 and 180:
ofthe distribution. The median surv
Page 181 and 182:
10.2.3 Weibull distribution Another
Page 183 and 184:
Table 10.1 Remission times of leuke
Page 185 and 186:
log H(y) 1 0 -1 -2 0 1 2 3 log (y)
Page 187 and 188:
As there are r uncensored observati
Page 189 and 190:
small number ofcategorical explanat
Page 191 and 192:
Cox Snell residuals 3 2 1 0 Devianc
Page 193 and 194:
is sometimes used for modelling sur
Page 195 and 196:
11 Clustered and Longitudinal Data
Page 197 and 198:
data from the stroke example in Sec
Page 199 and 200:
score 100 80 60 40 20 0 2 4 6 8 wee
Page 201 and 202:
Table11.3 Results of naive analyses
Page 203 and 204:
Table 11.6 Analysis of variance of
Page 205 and 206:
1. All the off-diagonal elements ar
Page 207 and 208:
These are also called the quasi-sco
Page 209 and 210:
andom effect.This is an example ofa
Page 211 and 212:
Table 11.7 Comparison of analyses o
Page 213 and 214:
Table 11.8 Measurements of left ven
Page 215 and 216:
Table 11.9 Numbers of ears clear of
Page 217 and 218:
References Aitkin, M., Anderson, D.
Page 219 and 220:
Diggle, P. J., Liang, K.-Y. and Zeg
Page 221:
Roberts, G., Martyn, A. L., Dobson,
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