Analysis of Categorical Data Under Logistic Regression Model
This chapter considers analysis of categorical data under logistic regression models when the data are generated from complex surveys. Section 6.2 addresses binary logistic regression model due to Roberts et al. (Biometrika 74:1–12, 1987), and finds the p
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Complex Surveys Analysis of Categorical Data
Complex Surveys
Parimal Mukhopadhyay
Complex Surveys Analysis of Categorical Data
123
Parimal Mukhopadhyay Indian Statistical Institute Kolkata, West Bengal India
ISBN 978-981-10-0870-2 DOI 10.1007/978-981-10-0871-9
ISBN 978-981-10-0871-9
(eBook)
Library of Congress Control Number: 2016936288 © Springer Science+Business Media Singapore 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
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Preface
Most of the data a statistician uses is categorical in nature. In the realms of biomedicine and social sciences, ecology and demography, voting pattern and marketing, to name a few, categorical data dominate. They are the major raw materials for analysis for testing different hypotheses relating to the populations which generate such data. Such data are generally obtained from surveys carried under a complex survey design, generally a stratified multistage design. In analysis of data collected through sample surveys, standard statistical techniques are often routinely employed. We recall the well-recited phrase which we chanted in our undergraduate days: Let x1,…, xn be a random sample of size n drawn from a population with probability density function f(x) or probability mass function pM(x), etc. This means that the sampled units whose observations are x1, x2,…, xn, are drawn by simple random sampling with replacement (srswr). This also implies that observed variables x1,…, xn are independently and identically distributed (IID). In fact, most of the results in theoretical statistics, including those in usual analysis of categorical data, are based on these assumptions. However, survey populations are often complex with different cell probabilities in different subgroups of the population, and this implies a situation different from th
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