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El. knyga: Generalized Estimating Equations

  • Formatas: PDF+DRM
  • Serija: Lecture Notes in Statistics 204
  • Išleidimo metai: 17-Jun-2011
  • Leidėjas: Springer-Verlag New York Inc.
  • Kalba: eng
  • ISBN-13: 9781461404996
Kitos knygos pagal šią temą:
Generalized Estimating EquationsDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Lecture Notes in Statistics 204
  • Išleidimo metai: 17-Jun-2011
  • Leidėjas: Springer-Verlag New York Inc.
  • Kalba: eng
  • ISBN-13: 9781461404996
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Generalized estimating equations have become increasingly popular in biometrical, econometrical, and psychometrical applications because they overcome the classical assumptions of statistics, i.e. independence and normality, which are too restrictive for many problems.

Therefore, the main goal of this book is to give a systematic presentation of the original generalized estimating equations (GEE) and some of its further developments. Subsequently, the emphasis is put on the unification of various GEE approaches. This is done by the use of two different estimation techniques, the pseudo maximum likelihood (PML) method and the generalized method of moments (GMM).

The author details the statistical foundation of the GEE approach using more general estimation techniques. The book could therefore be used as basis for a course to graduate students in statistics, biostatistics, or econometrics, and will be useful to practitioners in the same fields.



Generalized estimating equations have become increasingly popular in biometrical, econometrical and psychometrical applications. In this book, they are derived in a unified way using pseudo maximum likelihood estimation and the generalized method of moments.
Preface vii
1 The linear exponential family
1(10)
1.1 Definition
1(1)
1.2 Moments
2(1)
1.3 Parameterization in the mean
3(1)
1.4 Selected properties
3(2)
1.5 Examples for univariate linear exponential families
5(3)
1.6 Examples for multivariate linear exponential families
8(1)
1.7 Relationship to the parameterization in univariate generalized linear models
9(2)
2 The quadratic exponential family
11(10)
2.1 Definition
11(2)
2.2 Selected properties
13(1)
2.3 Examples for quadratic exponential families
13(1)
2.4 The joint distribution of dichotomous random variables
14(7)
2.4.1 The joint distribution of two dichotomous random variables
15(1)
2.4.2 The joint distribution of T dichotomous random variables
16(3)
2.4.3 Restriction of the parameter space in marginal models
19(2)
3 Generalized linear models
21(8)
3.1 Univariate generalized linear models
21(4)
3.1.1 Definition
21(1)
3.1.2 Parameterization and natural link function
22(1)
3.1.3 Examples
22(2)
3.1.4 Threshold model for dichotomous dependent data
24(1)
3.2 Multivariate generalized linear models
25(4)
3.2.1 Definition
25(1)
3.2.2 Examples
26(3)
4 Maximum likelihood method
29(22)
4.1 Definition
29(2)
4.2 Asymptotic properties
31(4)
4.3 Transformations
35(2)
4.4 Maximum likelihood estimation in linear exponential families
37(2)
4.5 Maximum likelihood estimation in generalized linear models
39(3)
4.5.1 Maximum likelihood estimation in univariate generalized linear models
40(1)
4.5.2 Maximum likelihood estimation in multivariate generalized linear models
41(1)
4.6 Maximum likelihood estimation under misspecified models
42(9)
4.6.1 An example for model misspecification
42(1)
4.6.2 Quasi maximum likelihood estimation
43(2)
4.6.3 The information matrix test
45(6)
5 Pseudo maximum likelihood method based on the linear exponential family
51(28)
5.1 Definition
52(2)
5.2 Asymptotic properties
54(5)
5.3 Examples
59(10)
5.3.1 Simple pseudo maximum likelihood 1 models
59(2)
5.3.2 Linear regression with heteroscedasticity
61(4)
5.3.3 Logistic regression with variance equal to 1
65(1)
5.3.4 Independence estimating equations with covariance matrix equal to identity matrix
66(2)
5.3.5 Generalized estimating equations 1 with fixed covariance matrix
68(1)
5.4 Efficiency and bias of the robust variance estimator
69(10)
5.4.1 Efficiency considerations
69(5)
5.4.2 Bias corrections and small sample adjustments
74(5)
6 Quasi generalized pseudo maximum likelihood method based on the linear exponential family
79(22)
6.1 Definition
80(1)
6.2 Asymptotic properties
81(5)
6.3 Examples
86(11)
6.3.1 Generalized estimating equations 1 with estimated working covariance matrix
89(1)
6.3.2 Independence estimating equations
90(1)
6.3.3 Generalized estimating equations 1 with estimated working correlation matrix
91(2)
6.3.4 Examples for working covariance and correlation structures
93(4)
6.4 Generalizations
97(4)
6.4.1 Time dependent parameters
97(1)
6.4.2 Ordinal dependent variables
98(3)
7 Pseudo maximum likelihood estimation based on the quadratic exponential family
101(18)
7.1 Definition
102(1)
7.2 Asymptotic properties
103(7)
7.3 Examples
110(9)
7.3.1 Generalized estimating equations 2 with an assumed normal distribution using the second centered moments
110(2)
7.3.2 Generalized estimating equations 2 for binary data or count data with an assumed normal distribution using the second centered moments
112(1)
7.3.3 Generalized estimating equations 2 with an arbitrary quadratic exponential family using the second centered moments
113(2)
7.3.4 Generalized estimating equations 2 for binary data using the second ordinary moments
115(4)
8 Generalized method of moment estimation
119(14)
8.1 Definition
119(1)
8.2 Asymptotic properties
120(2)
8.3 Examples
122(8)
8.3.1 Linear regression
122(1)
8.3.2 Independence estimating equations with covariance matrix equal to identity matrix
123(1)
8.3.3 Generalized estimating equations 1 with fixed working covariance matrix
123(1)
8.3.4 Generalized estimating equations 1 for dichotomous dependent variables with fixed working correlation matrix
124(1)
8.3.5 Generalized estimating equations 2 for binary data using the second ordinary moments
125(1)
8.3.6 Generalized estimating equations 2 using the second centered moments
126(1)
8.3.7 Generalized estimating equations 2 using the second standardized moments
126(2)
8.3.8 Alternating logistic regression
128(2)
8.4 Final remarks
130(3)
References 133(10)
Index 143
After studying statistics and mathematics at the University of Munich, Andreas Ziegler obtained his doctoral degree from the University of Dortmund (Germany) for his thesis on methodological developments on generalized estimating equations. In the past 15 years, he has authored or co-authored more than 300 journal articles and 6 books. He has received several awards for his methodological developments and collaborative studies in clinical trials and genetic epidemiology. Andreas Ziegler is professor and head of the Institute of Medical Biometry and Statistics at the University of Lübeck (Germany).
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