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E-grāmata: Analysis of Repeated Measures Data

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  • Formāts: PDF+DRM
  • Izdošanas datums: 06-Jul-2017
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789811037948
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Analysis of Repeated Measures DataPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 06-Jul-2017
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789811037948
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This book presents a broad range of statistical techniques to address emerging needs in the field of repeated measures. It also provides a comprehensive overview of extensions of generalized linear models for the bivariate exponential family of distributions, which represent a new development in analysing repeated measures data. The demand for statistical models for correlated outcomes has grown rapidly recently, mainly due to presence of two types of underlying associations: associations between outcomes, and associations between explanatory variables and outcomes.





The book systematically addresses key problems arising in the modelling of repeated measures data, bearing in mind those factors that play a major role in estimating the underlying relationships between covariates and outcome variables for correlated outcome data. In addition, it presents new approaches to addressing current challenges in the field of repeated measures and models based on conditional and joint probabilities. Markov models of first and higher orders are used for conditional models in addition to conditional probabilities as a function of covariates. Similarly, joint models are developed using both marginal-conditional probabilities as well as joint probabilities as a function of covariates. 





In addition to generalized linear models for bivariate outcomes, it highlights extended semi-parametric models for continuous failure time data and their applications in order to include models for a broader range of outcome variables that researchers encounter in various fields. The book further discusses the problem of analysing repeated measures data for failure time in the competing risk framework, which is now taking on an increasingly important role in the field of survival analysis, reliability and actuarial science. Details on how to perform the analyses are included in each chapter and supplemented with newly developed R packages and functions along with SAS codes and macro/IML. It is a valuable resource for researchers, graduate students and other users of statistical techniques for analysing repeated measures data.
1 Introduction
1(8)
2 Linear Models
9(14)
2.1 Simple Linear Regression Model
9(1)
2.2 Multiple Regression Model
10(1)
2.3 Estimation of Parameters
11(5)
2.3.1 Method of Least Squares
12(3)
2.3.2 Maximum Likelihood Estimation
15(1)
2.4 Tests
16(3)
2.5 Example
19(4)
3 Exponential Family of Distributions
23(8)
3.1 Exponential Family and Sufficiency
24(4)
3.2 Some Important Properties
28(3)
4 Generalized Linear Models
31(20)
4.1 Introduction
31(1)
4.2 Exponential Family and GLM
32(2)
4.3 Expected Value and Variance
34(1)
4.4 Components of a GLM
35(3)
4.5 Multinomial Response Model
38(2)
4.6 Estimating Equations
40(3)
4.7 Deviance
43(4)
4.8 Examples
47(4)
5 Covariate--Dependent Markov Models
51(16)
5.1 Introduction
51(1)
5.2 First Order Markov Model
52(2)
5.3 Conditional Model for Second Order Markov Chain with Covariate Dependence
54(3)
5.4 Covariate Dependent Model for Markov Chain of Order r
57(1)
5.5 Tests for the Model
58(2)
5.6 Examples
60(7)
6 Modeling Bivariate Binary Data
67(20)
6.1 Introduction
67(1)
6.2 Bivariate Bernoulli Distribution
68(1)
6.3 Bivariate Binary Model with Covariate Dependence
69(3)
6.3.1 Covariate-Dependent Model
70(1)
6.3.2 Likelihood Function and Estimating Equations
71(1)
6.4 Test for Dependence in Bivariate Binary Outcomes
72(4)
6.4.1 Measure of Dependence
72(1)
6.4.2 Test for the Model
73(2)
6.4.3 Test for Dependence
75(1)
6.5 Generalized Bivariate Bernoulli Model
76(6)
6.5.1 The Bivariate Bernoulli Model
77(2)
6.5.2 Estimating Equations
79(2)
6.5.3 Tests
81(1)
6.6 Some Alternative Binary Repeated Measures Models
82(2)
6.7 Examples
84(3)
7 Bivariate Geometric Model
87(10)
7.1 Introduction
87(1)
7.2 Univariate Geometric Distribution
88(1)
7.3 Bivariate Geometric Distribution: Marginal and Conditional Models
88(3)
7.4 Bivariate Geometric Distribution: Joint Model
91(2)
7.5 Examples
93(4)
8 Models for Bivariate Count Data: Bivariate Poisson Distribution
97(28)
8.1 Introduction
97(1)
8.2 The Poisson--Poisson Distribution
98(1)
8.3 Bivariate GLM for Poisson-Poisson
99(4)
8.3.1 Model and Estimation
99(1)
8.3.2 Overdispersion in Count Data
100(1)
8.3.3 Tests for Goodness of Fit
101(1)
8.3.4 Simple Tests for Overdispersion With or Without Covariate Dependence
102(1)
8.4 Zero-Truncated Bivariate Poisson
103(5)
8.4.1 Zero-Truncated Poisson Distribution
104(1)
8.4.2 A Generalized Zero-Truncated BVP Linear Model
105(2)
8.4.3 Test for the Model
107(1)
8.4.4 Deviance and Goodness of Fit
107(1)
8.5 Right-Truncated Bivariate Poisson Model
108(6)
8.5.1 Bivariate Right-Truncated Poisson-Poisson Model
108(2)
8.5.2 Predicted Probabilities
110(2)
8.5.3 Test for Goodness of Fit
112(2)
8.6 Double Poisson Distribution
114(7)
8.6.1 Double Poisson Model
114(4)
8.6.2 Bivariate Double Poisson Model
118(3)
8.7 Applications
121(4)
9 Bivariate Negative Binomial and Multinomial Models
125(14)
9.1 Introduction
125(1)
9.2 Review of GLM for Multinomial
126(2)
9.3 Bivariate Multinomial
128(3)
9.4 Tests for Comparison of Models
131(2)
9.5 Negative Multinomial Distribution and Bivariate GLM
133(4)
9.5.1 GLM for Negative Multinomial
134(3)
9.6 Application of Negative Multinomial Model
137(2)
10 Bivariate Exponential Model
139(12)
10.1 Introduction
139(1)
10.2 Bivariate Exponential Distributions
139(3)
10.3 Bivariate Exponential Generalized Linear Model
142(4)
10.4 Bivariate Exponential GLM Proposed by Iwasaki and Tsubaki
146(2)
10.5 Example
148(3)
11 Quasi-Likelihood Methods
151(10)
11.1 Introduction
151(1)
11.2 Likelihood Function and GLM
152(1)
11.3 Quasi-likelihood Functions
153(2)
11.4 Estimation of Parameters
155(3)
11.5 Examples
158(3)
12 Generalized Estimating Equation
161(8)
12.1 Introduction
161(1)
12.2 Background
161(2)
12.3 Estimation of Parameters
163(1)
12.4 Steps in a GEE: Estimation and Test
164(2)
12.5 Examples
166(3)
13 Generalized Linear Mixed Models
169(8)
13.1 Introduction
169(1)
13.2 Generalized Linear Mixed Model
169(1)
13.3 Identity Link Function
170(1)
13.4 Logit Link Function
170(1)
13.5 Log Link Function
171(2)
13.6 Multinomial Data
173(2)
13.7 Examples
175(2)
14 Generalized Multivariate Models
177(14)
14.1 Introduction
177(2)
14.2 Multivariate Poisson Distribution
179(2)
14.3 Multivariate Negative Binomial Distribution
181(1)
14.4 Multivariate Geometric Distribution
182(2)
14.5 Multivariate Normal Distribution
184(3)
14.6 Examples
187(4)
15 Multistate and Multistage Models
191(22)
15.1 Introduction
191(1)
15.2 Some Basic Concepts
192(4)
15.3 Censoring: Construction of Likelihood Function
196(1)
15.4 Proportional Hazards Model
197(2)
15.5 Competing Risk Proportional Hazards Model
199(1)
15.6 Multistate Hazards Model
200(3)
15.7 Multistage Hazards Model
203(4)
15.8 Examples
207(6)
16 Analysing Data Using R and SAS
213(22)
16.1 Description
213(22)
References 235(14)
Subject Index 249
M. Ataharul Islam is currently a professor at the Department of Applied Statistics, East West University, Bangladesh. He was a formerly professor of statistics at the Universiti Sains Malaysia, King Saud University and the University of Dhaka. He served as a visiting faculty at the University of Hawaii and University of Pennsylvania. He is a recipient of the Pauline Stitt Award, Western North American Region (WNAR) Biometric Society Award for content and writing, University Grants Commission Award for book and research, and the Ibrahim Memorial Gold Medal for research. He has published more than 100 papers in international journals on various topics, mainly on longitudinal and repeated measures data including multistate and multistage hazards model, statistical modelling, Markov models with covariate dependence, generalized linear models, conditional and joint models for correlated outcomes. He authored a book on Markov models, edited one book jointly and contributed chapters in several books. 





Rafiqul I. Chowdhury, a former senior lecturer at the Department of Health Information Administration, Kuwait University, Kuwait, has been involved widely in various research projects as a research collaborator and consultant. He has extensive experience in statistical computing with large data sets, specially, with repeated measures data. He has published more than 60 papers in international journals on statistical computing, repeated measures data and utilization of health care services among others and presented papers in various conferences. He co-authored a book on Markov models and wrote programs and developed packages for marginal, conditional and joint models including multistate Markov and hazards models, bivariate generalized linear models on Poisson, geometric, Bernoulli using SAS and R.
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