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.

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.

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