Antedependence Models for Longitudinal Data: 1st Edition (Paperback) book cover

Antedependence Models for Longitudinal Data

1st Edition

By Dale L. Zimmerman, Vicente A. Núñez-Antón

Chapman and Hall/CRC

288 pages | 28 B/W Illus.

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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.


"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 (, 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

Table of Contents


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


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



About the Authors/Editors

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.

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General