List of Figures p. xi
List of Tables p. xiii
List of Applications p. xv
List of Datasets p. xvii
Preface p. xix
Acknowledgments p. xxiii
Introduction p. 1
Generalized linear models for continuous/interval scale data p. 9
Introduction p. 9
Continuous/interval scale data p. 10
Simple and multiple linear regression models p. 11
Checking assumptions in linear regression models p. 12
Likelihood: multiple linear regression p. 13
Comparing model likelihoods p. 14
Application of a multiple linear regression model p. 15
Exercises on linear models p. 17
Generalized linear models for other types of data p. 21
Binary data p. 21
Introduction p. 21
Logistic regression p. 22
Logit and probit transformations p. 23
General logistic regression p. 24
Likelihood p. 24
Example with binary data p. 24
Ordinal data p. 26
Introduction p. 26
The ordered logit model p. 27
Dichotoinization of ordered categories p. 29
Likelihood p. 29
Example with ordered data p. 30
Count data p. 32
Introduction p. 32
Poisson regression models p. 33
Likelihood p. 34
Example with count data p. 34
Exercises p. 37
Family of generalized linear models p. 43
Introduction p. 43
The linear model p. 44
The binary response model p. 44
The Poisson model p. 46
Likelihood p. 46
Mixed models for continuous/interval scale data p. 49
Introduction p. 49
Linear mixed model p. 49
The intraclass correlation coefficient p. 51
Parameter estimation by maximum likelihood p. 53
Regression with level-two effects p. 54
Two-level random intercept models p. 55
General two-level models including random intercepts p. 56
Likelihood p. 58
Residuals p. 58
Checking assumptions in mixed models p. 59
Comparing model likelihoods p. 60
Application of a two-level linear model p. 61
Two-level growth models p. 66
A two-level repeated measures model p. 66
A linear growth model p. 66
A quadratic growth model p. 67
Likelihood p. 67
Example using linear growth models p. 68
Exercises using mixed models for continuous/interval scale data p. 69
Mixed models for binary data p. 75
Introduction p. 75
The two-level logistic model p. 75
General two-level logistic models p. 77
Intraclass correlation coefficient p. 77
Likelihood p. 78
Example using binary data p. 78
Exercises using mixed models for binary data p. 81
Mixed models for ordinal data p. 85
Introduction p. 85
The two-level ordered logit model p. 85
Likelihood p. 86
Example using mixed models for ordered data p. 87
Exercises using mixed models for ordinal data p. 90
Mixed models for count data p. 93
Introduction p. 93
The two-level Poisson model p. 93
Likelihood p. 94
Example using mixed models for count data p. 95
Exercises using mixed models for count data p. 97
Family of two-level generalized linear models p. 99
Introduction p. 99
The mixed linear model p. 100
The mixed binary response model p. 100
The mixed Poisson model p. 102
Likelihood p. 102
Three-level generalized linear models p. 105
Introduction p. 105
Three-level random intercept models p. 105
Three-level generalized linear models p. 106
Linear models p. 107
Binary response models p. 108
Likelihood p. 108
Example using three-level generalized linear models p. 109
Exercises using three-level generalized linear mixed models p. 112
Models for multivariate data p. 115
Introduction p. 115
Multivariate two-level generalized linear model p. 116
Bivariate Poisson model: example p. 117
Bivariate ordered response model: example p. 121
Bivariate linear-probit model: example p. 126
Multivariate two-level generalized linear model likelihood p. 131
Exercises using multivariate generalized linear mixed models p. 131
Models for duration and event history data p. 135
Introduction p. 135
Left censoring p. 135
Right censoring p. 135
Time-varying explanatory variables p. 136
Competing risks p. 136
Duration data in discrete time p. 137
Single-level models for duration data p. 137
Two-level models for duration data p. 139
Three-level models for duration data p. 140
Renewal data p. 143
Introduction p. 143
Example: renewal models p. 145
Competing risk data p. 147
Introduction p. 147
Likelihood p. 148
Example: competing risk data p. 150
Exercises using renewal and competing risks models p. 153
Stayers, non-susceptibles and endpoints p. 157
Introduction p. 157
Mover-stayer model p. 157
Likelihood incorporating the mover-stayer model p. 160
Example 1: stayers within count data p. 161
Example 2: stayers within binary data p. 164
Exercises: stayers p. 166
Handling initial conditions/state dependence in binary data p. 169
Introduction to key issues: heterogeneity, state dependence and non-stationarity p. 169
Example p. 170
Random effects models p. 171
Initial conditions problem p. 172
Initial treatment p. 173
Example: depression data p. 174
Classical conditional analysis p. 174
Classical conditional model: example p. 175
Conditioning on initial response but allowing random effect u0jto be dependent on Zj p. 176
Wooldridge conditional model: example p. 177
Modelling the initial conditions p. 178
Same random effect in the initial response and subsequent response models with a common scale parameter p. 179
Joint analysis with a common random effect: example p. 180
Same random effect in models of the initial response and subsequent responses but with different scale parameters p. 181
Joint analysis with a common random effect (different scale parameters): example p. 182
Different random effects in models of the initial response and subsequent responses p. 183
Different random effects: example p. 184
Embedding the Wooldridge approach in joint models for the initial response and subsequent responses p. 185
Joint model incorporating the Wooldridge approach: example p. 187
Other link functions p. 187
Exercises using models incorporating initial conditions/state dependence in binary data p. 188
Incidental parameters: an empirical comparison of fixed effects and random effects models p. 195
Introduction p. 195
Fixed effects treatment of the two-level linear model p. 197
Dummy variable specification of the fixed effects model p. 199
Empirical comparison of two-level fixed effects and random effects estimators p. 200
Implicit fixed effects estimator p. 204
Random effects models p. 204
Comparing two-level fixed effects and random effects models p. 208
Fixed effects treatment of the three-level linear model p. 208
Exercises comparing fixed effects and random effects p. 209
SabreR installation, SabreR commands, quadrature, estimation, endogenous effects p. 215
SabreR installation p. 215
SabreR commands p. 215
The arguments of the SabreR object p. 215
The anatomy of a SabreR command file p. 216
Quadrature p. 218
Standard Gaussian quadrature p. 218
Performance of Gaussian quadrature p. 219
Adaptive quadrature p. 221
Estimation p. 223
Maximizing the log likelihood of random effects models p. 223
Fixed effects linear models p. 225
Endogenous and exogenous variables p. 226
Introduction to R for Sabre p. 229
Getting started with R p. 229
Preliminaries p. 229
Working with R in interactive mode p. 229
Basic functions p. 231
Getting help p. 232
Stopping R p. 232
Creating and manipulating data p. 232
Vectors and lists p. 232
Vectors p. 233
Vector operations p. 234
Lists p. 235
Data frames p. 236
Session management p. 237
Managing objects p. 237
Attaching and detaching objects p. 237
Serialization p. 238
R scripts p. 238
Batch processing p. 239
R packages p. 239
Loading a package into R p. 239
Installing a package for use in R p. 239
R and Statistics p. 240
Data preparation for SabreR p. 240
Creation of dummy variables p. 240
Missing values p. 243
Creating lagged response covariate data p. 245
References p. 249
Author Index p. 259
Subject Index p. 263