Zimmerman D.L., Núñez-Antón V.A. Antedependence Models for Longitudinal Data

Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability (Book 112).
— Chapman & Hall/CRC, 2009. — 279 p. — ISBN: 1420064266, 978-1420064261.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.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.
Likelihood-Based Estimation.
Normal linear AD(p) model.
Estimation in the general case.
Unstructured antedependence: Balanced data.
Unstructured antedependence: Unbalanced data.
Structured antedependence models.
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.
Testing Hypotheses on the Mean Structure.
One-sample case.
Two-sample case.
Multivariate regression mean.
Other situations.
Penalized likelihood criteria.
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.