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Introduction
Generalized Linear Models for Continuous/Interval Scale
Data
Introduction
Continuous/interval scale data
Simple and multiple linear regression models
Checking assumptions in linear regression models
Likelihood: multiple linear regression
Comparing model likelihoods
Application of a multiple linear regression model
Generalized Linear Models for Other Types of
Data
Binary data
Ordinal data
Count data
Family of Generalized Linear Models
Introduction
The linear model
Binary response models
Poisson model
Likelihood
Mixed Models for Continuous/Interval Scale
Data
Introduction
Linear mixed model
The intraclass correlation coefficient
Parameter estimation by maximum likelihood
Regression with leveltwo effects
Twolevel random intercept models
General twolevel models including random intercepts
Likelihood
Residuals
Checking assumptions in mixed models
Comparing model likelihoods
Application of a twolevel linear model
Twolevel growth models
Likelihood
Example on linear growth models
Mixed Models for Binary Data
Introduction
The twolevel logistic model
General twolevel logistic models
Intraclass correlation coefficient
Likelihood
Example on binary data
Mixed Models for Ordinal Data
Introduction
The twolevel ordered logit model
Likelihood
Example on mixed models for ordered data
Mixed Models for Count Data
Introduction
The twolevel Poisson model
Likelihood
Example on mixed models for count data
Family of TwoLevel Generalized Linear
Models
Introduction
The mixed linear model
Mixed binary response models
Mixed Poisson model
Likelihood
ThreeLevel Generalized Linear Models
Introduction
Threelevel random intercept models
Threelevel generalized linear models
Linear models
Binary response models
Likelihood
Example on threelevel generalized linear models
Models for Multivariate Data
Introduction
Multivariate twolevel generalized linear model
Bivariate Poisson model: Example
Bivariate ordered response model: Example
Bivariate linearprobit model: Example
Multivariate twolevel generalized linear model likelihood
Models for Duration and Event History Data
Introduction
Duration data in discrete time
Renewal data
Competing risk data
Stayers, NonSusceptibles, and Endpoints
Introduction
Moverstayer model
Likelihood with moverstayer model
Example 1: Stayers in Poisson data
Example 2: Stayers in binary data
Handling Initial Conditions/State Dependence in Binary
Data
Introduction to key issues: heterogeneity, state
dependence and nonstationarity
Motivational example
Random effects model
Initial conditions problem
Initial treatment of initial conditions problem
Example: Depression data
Classical conditional analysis
Classical conditional model: Depression example
Conditioning on initial response but allowing random effect
u_{0j} to be dependent on
z_{j}
Wooldridge conditional model: Depression example
Modeling the initial conditions
Same random effect in the initial response and subsequent response
models with a common scale parameter
Joint analysis with a common random effect: Depression example
Same random effect in models of the initial response and subsequent
responses but with different scale parameters
Joint analysis with a common random effect (different scale
parameters): Depression example
Different random effects in models of the initial response and
subsequent responses
Different random effects: Depression example
Embedding the Wooldridge approach in joint models for the initial
response and subsequent responses
Joint model plus the Wooldridge approach: Depression example
Other link functions
Incidental Parameters: An Empirical Comparison of Fixed
Effects and Random Effects Models
Introduction
Fixed effects treatment of the twolevel linear model
Dummy variable specification of the fixed effects model
Empirical comparison of twolevel fixed effects and random effects
estimators
Implicit fixed effects estimator
Random effects models
Comparing twolevel fixed effects and random effects models
Fixed effects treatment of the threelevel linear model
Appendix A: SabreR Installation, SabreR Commands,
Quadrature, Estimation, Endogenous Effects
Appendix B: Introduction to R for Sabre
Bibliography
Exercises appear at the end of most chapters.
Damon M. Berridge is a senior lecturer in the Department of Mathematics and Statistics at Lancaster University. Dr. Berridge has nearly 20 years of experience as a statistical consultant. His research focuses on the modeling of binary and ordinal recurrent events through random effects models, with application in medical and social statistics. Robert Crouchley is a professor of applied statistics and director of the Centre for eScience at Lancaster University. His research interests involve the development of statistical methods and software for causal inference in nonexperimental data. These methods include models for errors in variables, missing data, heterogeneity, state dependence, nonstationarity, event history data, and selection effects.
I think this is a very well organised and written book and
therefore I highly recommend it not only to professionals and
students but also to applied researchers from many research areas
such as education, psychology and economics working on complex and
large data sets.
Sebnem Er, Journal of Applied Statistics, 2012
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