1st Edition
Antedependence Models for Longitudinal Data
The First Book Dedicated to This Class of Longitudinal Models
Although antedependence models are particularly useful for modeling longitudinal data that exhibit serial correlation, few books adequately cover these models. By gathering results scattered throughout the literature, Antedependence Models for Longitudinal Data offers a convenient, systematic way to learn about antedependence models. Illustrated with numerous examples, the book also covers some important statistical inference procedures associated with these models.
After describing unstructured and structured antedependence models and their properties, the authors discuss informal model identification via simple summary statistics and graphical methods. They then present formal likelihood-based procedures for normal antedependence models, including maximum likelihood and residual maximum likelihood estimation of parameters as well as likelihood ratio tests and penalized likelihood model selection criteria for the model’s covariance structure and mean structure. The authors also compare the performance of antedependence models to other models commonly used for longitudinal data.
With this book, readers no longer have to search across widely scattered journal articles on the subject. The book provides a thorough treatment of the properties and statistical inference procedures of various antedependence models.
Introduction
Longitudinal data
Classical methods of analysis
Parametric modeling
Antedependence models, in brief
A motivating example
Overview of the book
Four featured data sets
Unstructured Antedependence Models
Antedependent random variables
Antecorrelation and partial antecorrelation
Equivalent characterizations
Some results on determinants and traces
The first-order case
Variable-order antedependence
Other conditional independence models
Structured Antedependence Models
Stationary autoregressive models
Heterogeneous autoregressive models
Integrated autoregressive models
Integrated antedependence models
Unconstrained linear models
Power law models
Variable-order SAD models
Nonlinear stationary autoregressive models
Comparisons with other models
Informal Model Identification
Identifying mean structure
Identifying covariance structure: summary statistics
Identifying covariance structure: graphical methods
Concluding remarks
Likelihood-Based Estimation
Normal linear AD(p) model
Estimation in the general case
Unstructured antedependence: balanced data
Unstructured antedependence: unbalanced data
Structured antedependence models
Concluding remarks
Testing Hypotheses on the Covariance Structure
Tests on individual parameters
Testing for the order of antedependence
Testing for structured antedependence
Testing for homogeneity across groups
Penalized likelihood criteria
Concluding remarks
Testing Hypotheses on the Mean Structure
One-sample case
Two-sample case
Multivariate regression mean
Other situations
Penalized likelihood criteria
Concluding remarks
Case Studies
A coherent parametric modeling approach
Case study #1: Cattle growth data
Case study #2: 100-km race data
Case study #3: Speech recognition data
Case study #4: Fruit fly mortality data
Other studies
Discussion
Further Topics and Extensions
Alternative estimation methods
Nonlinear mean structure
Discrimination under antedependence
Multivariate antedependence models
Spatial antedependence models
Antedependence models for discrete data
Appendix 1: Some Matrix Results
Appendix 2: Proofs of Theorems 2.5 and 2.6
References
Index
Biography
Dale L. Zimmerman is a professor in the Department of Statistics and Actuarial Science at the University of Iowa.
Vicente A. Núnez-Antón is a professor in the Department of Econometrics and Statistics at The University of the Basque Country.
"The book is well written and clearly arranged and can be recommended to statisticians with interest in longitudinal data."
—P.G. Hackl, Statistical Papers (2013) 54"When we fit models to describe a data, we try different models to determine a model that would describe the data better than the other models. This book provides a class of antedependence models to try. The authors made a valuable contribution to our profession by providing in this book some possible models along with the inference procedures for us to try to describe a longitudinal data better."
—Subir Ghosh, Technometrics, May 2012"The motivation for this work was the authors’ view that such covariance structures have a much greater role to play in the analysis of longitudinal data than is commonly realized and that for ‘antedependence models to realize their full potential … this body of work needs to be brought together in one place…’. They have managed to achieve this aim both thoroughly and effectively. … this monograph provides a thorough treatment of the antedependence covariance structure in all its various forms and clearly illustrates its use in a variety of longitudinal settings."
—Australian & New Zealand Journal of Statistics, 53(1), 2011"This book is the first one dedicated entirely to antedependece models … The material presented is well organized. … Several relevant R functions are available for download from the first author’s webpage (http://www.stat.uiowa.edu/~dzimmer), and the authors are making available and documenting more in the near future. This is very important for applications, since there is little software developed for these models, and applied researchers will be very satisfied with the availability of R functions to fit antedependence models to their data. … the book is very useful as a supplementary material in a course on longitudinal data analysis, or it could be the basis of a special topics course on antedependence models. In summary, this book is a welcome addition to the bibliography of longitudinal data, combining rigorous statistical presentation with interesting real life examples."
—Raúl E. Macchiavelli, SORT, Vol. 34 (1), 2010"The main problems which need to be addressed in the context of longitudinal data analysis are mean and covariance specification. This text offers a fresh point of view to both of these issues. The textbook presents a detailed investigation of the class of antedependence models for modelling normally distributed longitudinal data. … I enjoyed reading the book and I believe that this work is a useful addition to the texts on longitudinal data analysis. … The main concepts and ideas are presented smoothly and without any ambiguities. This book is suitable as a supplement text for an advanced graduate course or for self-study by doctoral students or researchers in statistics and biostatistics. … an excellent addition to the literature and I recommend it to any professional statistician."
—Journal of Time Series Analysis, 2010
