Overview of Linear Fixed Models for Longitudinal Data
In a longitudinal setup, a small number of repeated responses along with certain multidimensional covariates are collected from a large number of independent individuals. Let y yi1, …,y it , …,y iT i be T i ≥ 2 repeated responses collected from the ith in
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Brajendra C. Sutradhar
Dynamic Mixed Models for Familial Longitudinal Data
Brajendra C. Sutradhar Department of Mathematics and Statistics Memorial University A1C 5S7 Saint John’s Newfoundland and Labrador Canada [email protected]
ISSN 0172-7397 ISBN 978-1-4419-8341-1 e-ISBN 978-1-4419-8342-8 DOI 10.1007/978-1-4419-8342-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011921116 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Bhagawan Sri Sathya Sai Baba my Guru, Mother and Father [Twameva Guru Cha Mata Twameva Twameva Guru Cha Pita Twameva Twameva Sarvam Mama Deva Deva]
Preface Discrete familial data consist of count or binary responses along with suitable covariates from the members of a large number of independent families, whereas discrete longitudinal data consist of similar responses and covariates collected repeatedly over a small period of time from a large number of independent individuals. As the statistical modelling of correlation structures especially for the discrete longitudinal data has not been easy, many researchers over the last two decades have used either certain ‘working’ models or mixed (familial) models for the analysis of discrete longitudinal data. Many books are also written reflecting these ‘working’ or mixed models based research. This book, however, presents a clear difference between the modelling of familial and longitudinal data. Parametric or semiparametric mixed models are used to analyze familial data, whereas parametric dynamic models are exploited to analyze the longitudinal data. Consequently, dynamic mixed models are used to analyze combined familial longitudinal data. Basic properties of the models are discussed in detail. As far as the inferences are concerned, various types of consistent estimators are considered, including simple ones based on method of moments, quasi-likelihood, and weighted least squares, and more efficient ones such as generalized quasi-likelihood estimators which account for the underlying familial and/or longitudinal correlation structure of the data. Special care is given to the mathematical derivation of the estim
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