Zimmerman / Núñez-Antón Antedependence Models for Longitudinal Data

Erscheinungsjahr 2010
ISBN: 978-1-4200-6427-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 288 Seiten

Reihe: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

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.

Zielgruppe

Researchers, practitioners, and graduate students in statistics and biostatistics; quantitative researchers in biology, epidemiology and public health, human medicine, veterinary medicine, animal science, agronomy, forestry, and genetics.

Autoren/Hrsg.

Zimmerman, Dale L.

Núñez-Antón, Vicente A.

Fachgebiete

• Naturwissenschaften Biowissenschaften Biowissenschaften
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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

Über Autor(innen)

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.