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Dynamic Mixed Models for Familial Longitudinal Data 2011 ed. [Kietas viršelis]

  • Formatas: Hardback, 494 pages, aukštis x plotis: 235x155 mm, weight: 1960 g, XVIII, 494 p., 1 Hardback
  • Serija: Springer Series in Statistics
  • Išleidimo metai: 03-Feb-2011
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1441983414
  • ISBN-13: 9781441983411
Kitos knygos pagal šią temą:
Dynamic Mixed Models for Familial Longitudinal Data 2011 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 494 pages, aukštis x plotis: 235x155 mm, weight: 1960 g, XVIII, 494 p., 1 Hardback
  • Serija: Springer Series in Statistics
  • Išleidimo metai: 03-Feb-2011
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1441983414
  • ISBN-13: 9781441983411
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781441983411.html
Raktažodžiai:
This book provides a theoretical foundation for the analysis of discrete data such as count and binary data in the longitudinal setup. Unlike the existing books, this book uses a class of auto-correlation structures to model the longitudinal correlations for the repeated discrete data that accommodates all possible Gaussian type auto-correlation models as special cases including the equi-correlation models. This new dynamic modelling approach is utilized to develop theoretically sound inference techniques such as the generalized quasi-likelihood (GQL) technique for consistent and efficient estimation of the underlying regression effects involved in the model, whereas the existing working correlations based GEE (generalized estimating equations) approach has serious theoretical limitations both for consistent and efficient estimation, and the existing random effects based correlations approach is not suitable to model the longitudinal correlations. The book has exploited the random effects carefully only to model the correlations of the familial data. Subsequently, this book has modelled the correlations of the longitudinal data collected from the members of a large number of independent families by using the class of auto-correlation structures conditional on the random effects. The book also provides models and inferences for discrete longitudinal data in the adaptive clinical trial set up. The book is mathematically rigorous and provides details for the development of estimation approaches under selected familial and longitudinal models. Further, while the book provides special cares for mathematics behind the correlation models, it also presents the illustrations of the statistical analysis of various real life data. This book will be of interest to the researchers including graduate students in biostatistics and econometrics, among other applied statistics research areas. Brajendra Sutradhar is a University ResearchProfessor at Memorial University in St. Johns, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to the society including his special services for societys annual meetings.

Recenzijos

This is a great book on the combination of longitudinal and familial data in the framework of the generalized linear model. the book provides an extremely valuable description of complex models in a very logical and understandable way. I strongly recommend it to all researchers dealing with longitudinal familial data with the primary aim of estimating the mean structure by parametric regression models. (Andreas Ziegler, Biometrical Journal, Vol. 56 (1), 2014)

This book describes models that deal with discrete familial data. The content is detailed and supported by up-to-date references, many of which are from the author himself, who is an expert in the field. The style is technical, making this book a useful reference for researchers in the area of quasi-likelihood estimation. In addition, this book can also be used as a textbook for graduate courses or for statisticians interested in familial data. (Vassilis G. S. Vasdekis, Mathematical Reviews, Issue 2012 c)

1 Introduction
1(8)
1.1 Background of Familial Models
1(2)
1.2 Background of Longitudinal Models
3(3)
References
6(3)
2 Overview of Linear Fixed Models for Longitudinal Data
9(20)
2.1 Estimation of β
10(4)
2.1.1 Method of Moments (MM)
10(1)
2.1.2 Ordinary Least Squares (OLS) Method
11(2)
2.1.3 OLS Versus GLS Estimation Performance
13(1)
2.2 Estimation of β Under Stationary General Autocorrelation Structure
14(5)
2.2.1 A Class of Autocorrelations
14(4)
2.2.2 Estimation of β
18(1)
2.3 A Rat Data Example
19(4)
2.4 Alternative Modelling for Time Effects
23(1)
Exercises
24(2)
References
26(3)
3 Overview of Linear Mixed Models for Longitudinal Data
29(30)
3.1 Linear Longitudinal Mixed Model
30(6)
3.1.1 GLS Estimation of β
31(1)
3.1.2 Moment Estimating Equations for σ 2 γ and ρl
32(1)
3.1.3 Linear Mixed Models for Rat Data
33(3)
3.2 Linear Dynamic Mixed Models for Balanced Longitudinal Data
36(6)
3.2.1 Basic Properties of the Dynamic Dependence Mixed Model (3.21)
37(1)
3.2.2 Estimation of the Parameters of the Dynamic Mixed Model (3.21)
38(4)
3.3 Further Estimation for the Parameters of the Dynamic Mixed Model
42(13)
3.3.1 GMM/IMM Estimation Approach
43(5)
3.3.2 GQL Estimation Approach
48(4)
3.3.3 Asymptotic Efficiency Comparison
52(3)
Exercises
55(2)
References
57(2)
4 Familial Models for Count Data
59(60)
4.1 Poisson Mixed Models and Basic Properties
60(3)
4.2 Estimation for Single Random Effect Based Parametric Mixed Models
63(31)
4.2.1 Exact Likelihood Estimation and Drawbacks
63(2)
4.2.2 Penalized Quasi-Likelihood Approach
65(3)
4.2.3 Small Variance Asymptotic Approach: A Likelihood Approximation (LA)
68(7)
4.2.4 Hierarchical Likelihood (HL) Approach
75(2)
4.2.5 Method of Moments (MM)
77(1)
4.2.6 Generalized Quasi-Likelihood (GQL) Approach
78(7)
4.2.7 Efficiency Comparison
85(6)
4.2.8 A Health Care Data Utilization Example
91(3)
4.3 Estimation for Multiple Random Effects Based Parametric Mixed Models
94(10)
4.3.1 Random Effects in a Two-Way Factorial Design Setup
94(1)
4.3.2 One-Way Heteroscedastic Random Effects
94(1)
4.3.3 Multiple Independent Random Effects
95(9)
4.4 Semiparametric Approach
104(7)
4.4.1 Computations for μi, λi, Σi, and Ωi
107(3)
4.4.2 Construction of the Estimating Equation for β When σ 2 γ Is Known
110(1)
4.5 Monte Carlo Based Likelihood Estimation
111(3)
4.5.1 MCEM Approach
113(1)
4.5.2 MCNR Approach
113(1)
Exercises
114(3)
References
117(2)
5 Familial Models for Binary Data
119(62)
5.1 Binary Mixed Models and Basic Properties
120(4)
5.1.1 Computational Formulas for Binary Moments
123(1)
5.2 Estimation for Single Random Effect Based Parametric Mixed Models
124(22)
5.2.1 Method of Moments (MM)
124(2)
5.2.2 An Improved Method of Moments (IMM)
126(5)
5.2.3 Generalized Quasi-Likelihood (GQL) Approach
131(4)
5.2.4 Maximum Likelihood (ML) Estimation
135(3)
5.2.5 Asymptotic Efficiency Comparison
138(5)
5.2.6 COPD Data Analysis: A Numerical Illustration
143(3)
5.3 Binary Mixed Models with Multidimensional Random Effects
146(18)
5.3.1 Models in Two-Way Factorial Design Setup and Basic Properties
146(3)
5.3.2 Estimation of Parameters
149(11)
5.3.3 Salamander Mating Data Analysis
160(4)
5.4 Semiparametric Approach
164(5)
5.4.1 GQL Estimation
164(2)
5.4.2 A Marginal Quasi-Likelihood (MQL) Approach
166(1)
5.4.3 Asymptotic Efficiency Comparison: An Empirical Study
167(2)
5.5 Monte Carlo Based Likelihood Estimation
169(1)
Exercises
169(3)
References
172(2)
Appendix
174(7)
6 Longitudinal Models for Count Data
181(60)
6.1 Marginal Model
182(1)
6.2 Marginal Model Based Estimation of Regression Effects
183(2)
6.3 Correlation Models for Stationary Count Data
185(3)
6.3.1 Poisson AR(1) Model
186(1)
6.3.2 Poisson MA(1) Model
187(1)
6.3.3 Poisson Equicorrelation Model
187(1)
6.4 Inferences for Stationary Correlation Models
188(13)
6.4.1 Likelihood Approach and Complexity
188(1)
6.4.2 GQL Approach
189(7)
6.4.3 GEE Approach and Limitations
196(5)
6.5 Nonstationary Correlation Models
201(8)
6.5.1 Nonstationary Correlation Models with the Same Specified Marginal Mean and Variance Functions
202(3)
6.5.2 Estimation of Parameters
205(2)
6.5.3 Model Selection
207(2)
6.6 More Nonstationary Correlation Models
209(8)
6.6.1 Models with Variable Marginal Means and Variances
209(2)
6.6.2 Estimation of Parameters
211(2)
6.6.3 Model Selection
213(2)
6.6.4 Estimation and Model Selection: A Simulation Example
215(2)
6.7 A Data Example: Analyzing Health Care Utilization Count Data
217(2)
6.8 Models for Count Data from Longitudinal Adaptive Clinical Trials
219(12)
6.8.1 Adaptive Longitudinal Designs
220(4)
6.8.2 Performance of the SLPW and BRW Designs For Treatment Selection: A Simulation Study
224(3)
6.8.3 Weighted GQL Estimation for Treatment Effects and Other Regression Parameters
227(4)
Exercises
231(3)
References
234(2)
Appendix
236(5)
7 Longitudinal Models for Binary Data
241(80)
7.1 Marginal Model
243(2)
7.1.1 Marginal Model Based Estimation for Regression Effects
244(1)
7.2 Some Selected Correlation Models for Longitudinal Binary Data
245(11)
7.2.1 Bahadur Multivariate Binary Density (MBD) Based Model
246(3)
7.2.2 Kanter Observation-Driven Dynamic (ODD) Model
249(3)
7.2.3 A Linear Dynamic Conditional Probability (LDCP) Model
252(2)
7.2.4 A Numerical Comparison of Range Restrictions for Correlation Index Parameter Under Stationary Binary Models
254(2)
7.3 Low-Order Autocorrelation Models for Stationary Binary Data
256(10)
7.3.1 Binary AR(1) Model
256(1)
7.3.2 Binary MA(1) Model
256(3)
7.3.3 Binary Equicorrelation (EQC) Model
259(1)
7.3.4 Complexity in Likelihood Inferences Under Stationary Binary Correlation Models
260(1)
7.3.5 GQL Estimation Approach
261(3)
7.3.6 GEE Approach and Its Limitations for Binary Data
264(2)
7.4 Inferences in Nonstationary Correlation Models for Repeated Binary Data
266(8)
7.4.1 Nonstationary AR(1) Correlation Model
266(2)
7.4.2 Nonstationary MA(1) Correlation Model
268(1)
7.4.3 Nonstationary EQC Model
269(1)
7.4.4 Nonstationary Correlations Based GQL Estimation
270(3)
7.4.5 Model Selection
273(1)
7.5 SLID Data Example
274(4)
7.5.1 Introduction to the SLID Data
274(2)
7.5.2 Analysis of the SLID Data
276(2)
7.6 Application to an Adaptive Clinical Trial Setup
278(12)
7.6.1 Binary Response Based Adaptive Longitudinal Design
278(7)
7.6.2 Construction of the Adaptive Design Weights Based Weighted GQL Estimation
285(5)
7.7 More Nonstationary Binary Correlation Models
290(24)
7.7.1 Linear Binary Dynamic Regression (LBDR) Model
290(5)
7.7.2 A Binary Dynamic Logit (BDL) Model
295(12)
7.7.3 Application of the Binary Dynamic Logit (BDL) Model in an Adaptive Clinical Trial Setup
307(7)
Exercises
314(2)
References
316(2)
Appendix
318(3)
8 Longitudinal Mixed Models for Count Data
321(68)
8.1 A Conditional Serially Correlated Model
321(2)
8.2 Parameter Estimation
323(25)
8.2.1 Estimation of the Regression Effects β
324(8)
8.2.2 Estimation of the Random Effects Variance σ2γ
332(5)
8.2.3 Estimation of the Longitudinal Correlation Parameter ρ
337(2)
8.2.4 A Simulation Study
339(7)
8.2.5 An Illustration: Analyzing Health Care Utilization Count Data by Using Longitudinal Fixed and Mixed Models
346(2)
8.3 A Mean Deflated Conditional Serially Correlated Model
348(14)
8.4 Longitudinal Negative Binomial Fixed Model and Estimation of Parameters
362(13)
8.4.1 Inferences in Stationary Negative Binomial Correlation Models
363(4)
8.4.2 A Data Example: Analyzing Epileptic Count Data by Using Poisson and Negative Binomial Longitudinal Models
367(2)
8.4.3 Nonstationary Negative Binomial Correlation Models and Estimation of Parameters
369(6)
Exercises
375(2)
References
377(2)
Appendix
379(10)
9 Longitudinal Mixed Models for Binary Data
389(34)
9.1 A Conditional Serially Correlated Model
390(6)
9.1.1 Basic Properties of the Model
390(2)
9.1.2 Parameter Estimation
392(4)
9.2 Binary Dynamic Mixed Logit (BDML) Model
396(19)
9.2.1 GMM/IMM Estimation
398(5)
9.2.2 GQL Estimation
403(2)
9.2.3 Efficiency Comparison: GMM Versus GQL
405(4)
9.2.4 Fitting the Binary Dynamic Mixed Logit Model to the SLID data
409(2)
9.2.5 GQL Versus Maximum Likelihood (ML) Estimation for BDML Model
411(4)
9.3 A Binary Dynamic Mixed Probit (BDMP) Model
415(5)
9.3.1 GQL Estimation for BDMP Model
416(1)
9.3.2 GQL Estimation Performance for BDMP Model: A Simulation Study
417(3)
Exercises
420(1)
References
421(2)
10 Familial Longitudinal Models for Count Data
423(32)
10.1 An Autocorrelation Class of Familial Longitudinal Models
423(6)
10.1.1 Marginal Mean and Variance
424(1)
10.1.2 Nonstationary Autocorrelation Models
425(4)
10.2 Parameter Estimation
429(17)
10.2.1 Estimation of Parameters Under Conditional AR(1) Model
430(9)
10.2.2 Performance of the GQL Approach: A Simulation Study
439(7)
10.3 Analyzing Health Care Utilization Data by Using GLLMM
446(3)
10.4 Some Remarks on Model Identification
449(2)
10.4.1 An Exploratory Identification
450(1)
10.4.2 A Further Improved Identification
451(1)
Exercises
451(2)
References
453(2)
11 Familial Longitudinal Models for Binary Data
455(34)
11.1 LDCCP Models
456(12)
11.1.1 Conditional-Conditional (CC) AR(1) Model
456(2)
11.1.2 CC MA(1) Model
458(1)
11.1.3 CC EQC Model
459(1)
11.1.4 Estimation of the AR(1) Model Parameters
460(8)
11.2 Application to Waterloo Smoking Prevention Data
468(3)
11.3 Family Based BDML Models for Binary Data
471(12)
11.3.1 FBDML Model and Basic Properties
472(2)
11.3.2 Quasi-Likelihood Estimation in the Familial Longitudinal Setup
474(5)
11.3.3 Likelihood Based Estimation
479(4)
Exercises
483(4)
Reference
487(2)
Index 489
Brajendra Sutradhar is a University Research Professor at Memorial University in St. John's, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded the 2007 distinguished service award of Statistics Society of Canada for his many years of services to the society including his special services for society's annual meetings.