Analysis of Longitudinal Data

by Diggle, Peter J.; Liang, Kung-Yee; Zeger, Scott L.

• ISBN13: 9780198522843
• ISBN10: 0198522843
• Format: Hardcover
• Copyright: 1994-08-25
• Publisher: Oxford University Press

Summary

This book provides a self-contained account of a wide range of statistical methods for the analysis of longitudinal data. Emphasizing the biomedical and agricultural sciences, the book covers each method's applicability and underlying statistical theory. Major topics include: design considerations, exploratory methods of analysis, linear models for continuous data, generalized linear models for discrete data, and models and methods for handling data with missing values. Worked examples are presented throughout and an appendix covers some basic statistical principles. This cogent and clear text will be welcomed by students across a wide range of the sciences.

Table of Contents

Introduction	1	(22)
Longitudinal studies	1	(2)
Examples	3	(13)
Notation	16	(1)
Merits of longitudinal studies	17	(1)
Approaches to longitudinal data analysis	18	(3)
Organization of subsequent chapters	21	(2)
Design considerations	23	(10)
Introduction	23	(1)
Bias	23	(2)
Efficiency	25	(2)
Sample size calculations	27	(5)
Continuous responses	29	(2)
Binary responses	31	(1)
Further reading	32	(1)
Exploring longitudinal data	33	(22)
Introduction	33	(1)
Graphical presentation of longitudinal data	34	(7)
Fitting smooth curves to longitudinal data	41	(6)
Exploring correlation structure	47	(5)
Further reading	52	(3)
General linear models for longitudinal data	55	(23)
Motivation	55	(1)
The general linear model with correlated errors	55	(3)
The uniform correlation model	56	(1)
The exponential correlation model	57	(1)
Weighted least-squares estimation	58	(5)
Maximum likelihood estimation under Gaussian assumptions	63	(1)
Restricted maximum likelihood estimation	64	(4)
Robust estimation of standard errors	68	(10)
Parametric models for covariance structure	78	(39)
Introduction	78	(1)
Models	79	(11)
Pure serial correlation	81	(6)
Serial correlation plus measurement error	87	(1)
Random intercept plus serial correlation plus measurement error	87	(1)
Random effects plus measurement error	88	(2)
Model-fitting	90	(5)
Formulation	91	(1)
Estimation	92	(1)
Inference	93	(2)
Diagnostics	95	(1)
Examples	95	(11)
Non-parametric modelling of the mean response	106	(7)
Estimation of individual trajectories	113	(2)
Further reading	115	(2)
Analysis of variance methods	117	(14)
Preliminaries	117	(1)
Time-by-time ANOVA	118	(4)
Derived variables	122	(4)
Repeated measures	126	(3)
Conclusions	129	(2)
Generalized linear models for longitudinal data	131	(15)
Marginal models	131	(2)
Random effects models	133	(2)
Transition (Markov) models	135	(2)
Contrasting approaches	137	(5)
Inferences	142	(4)
Marginal models	146	(23)
Introduction	146	(1)
Binary responses	147	(6)
The log-linear model	147	(1)
Log-linear models for marginal means	148	(3)
Generalized estimating equations	151	(2)
Examples	153	(9)
Counted responses	162	(5)
Parametric modelling for count data	162	(3)
Generalized estimating equation approach	165	(1)
An example	165	(2)
Further reading	167	(2)
Random effects models	169	(21)
Introduction	169	(2)
Estimation for generalized linear mixed models	171	(4)
Conditional likelihood	171	(1)
Maximum likelihood estimation	172	(3)
Logistic regression for binary responses	175	(8)
Conditional likelihood approach	175	(3)
Random effects models for binary data	178	(2)
Examples of logistic models with Gaussian random effects	180	(3)
Counted responses	183	(5)
Conditional likelihood method	183	(2)
Random effects models for counts	185	(2)
Poisson--Gaussian random effects models	187	(1)
Further reading	188	(2)
Transition models	190	(18)
General	190	(2)
Fitting transition models	192	(2)
Transition models for categorical data	194	(9)
Indonesian children's study example	197	(4)
Ordered categorical data	201	(2)
Log-linear transition models for count data	203	(4)
Further reading	207	(1)
Missing values in longitudinal data	208	(27)
Classification of missing values for longitudinal data	208	(3)
Testing for completely random dropouts	211	(5)
Modelling the dropout process	216	(5)
Discussion	221	(14)
A Statistical Background	235	(12)
A.1 Introduction	235	(1)
A.2 The linear model and the method of least squares	235	(2)
A.3 Multivariate Gaussian theory	237	(1)
A.4 Likelihood inference	238	(3)
A.5 Generalized linear models	241	(3)
A.5.1 Logistic regression	241	(1)
A.5.2 Poisson regression	242	(1)
A.5.3 The general class	243	(1)
A.6 Quasi-likelihood	244	(3)
Index	247