1st Edition

Antedependence Models for Longitudinal Data

    288 Pages 28 B/W Illustrations
    by Chapman & Hall

    288 Pages 28 B/W Illustrations
    by Chapman & Hall

    Continue Shopping

    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

    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




    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