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INTRODUCING QUANTITATIVE GEOGRAPHY A VOLUME IN THE ROUTLEDGE GEOGRAPHY AND ENVIRONMENT SERIES Edited by Michael Bradford INTRODUCING QUANTITATIVE GEOGRAPHY Measurement, methods and generalised linear models Larry O’Brien London and New York First published 1992 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “ To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.” Simultaneously published in the USA and Canada by Routledge a division of Routledge, Chapman and Hall, Inc. 29 West 35th Street, New York, NY 10001 © 1992 Larry O’Brien All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this title is available from the British Library. Library of Congress Cataloging in Publication Data O’Brien, Larry, 1957– Introducing quantitative geography: measurement, methods, and generalised linear models/Larry O’Brien. p. cm.—(Geography and environment series) Includes bibliographical references and index. ISBN 0415-00465-9 (HB).—ISBN 0-415-07558-0 (pbk.) 1. Geography—Mathematics. I. Title. II. Series. G70.23.036 1992 910′.015′1–dc20 91–28683 CIP ISBN 0-203-97335-6 Master e-book ISBN ISBN 0-415-00465-9 (Print Edition) CONTENTS List of illustrations vi List of tables xi Preface 1 INTRODUCTION xviii 1 Part I Preliminaries: geographical data and data handling 2 DESCRIBING GEOGRAPHICAL DATA 8 3 MEASURING GEOGRAPHICAL DATA 32 4 SUMMARISING GEOGRAPHICAL DATA 43 5 DESCRIPTIVE MODELS AND GEOGRAPHICAL DATA 91 6 STATISTICAL INFERENCE 117 Part II Generalised linear modelling 7 TOWARDS INTEGRATION—GENERALISED LINEAR 161 MODELS 8 GENERALISED LINEAR MODELS FOR CONTINUOUS DATA 181 9 GENERALISED LINEAR MODELS FOR CATEGORICAL DATA 10 SOME EXTENSIONS AND SPECIALISED TOPICS 228 11 SUMMARY AND CONCLUSIONS 311 287 Appendix The exponential family of probability distributions A 319 Appendix Other software for modelling and geographical data analysis B 323 Appendix C A summary of the GLIM 3 command language 325 Bibliography 331 Index 344 ILLUSTRATIONS FIGURES 1.1 Some generalised linear models used in geography 3 2.1 Retail provision in eastern Reading, UK 19 2.2 Distribution of the elderly by region 21 2.3 Distribution of the elderly by county 22 2.4 Distribution of the elderly in East Sussex by ward 23 2.5 ‘Equal levels’ map of data in Table 2.6 27 2.6 ‘Quantile’ map of data in Table 2.6 28 2.7 ‘Arithmetic progression’ map of data in Table 2.6 29 3.1 Examples of an ordinal scale 37 3.2 Example of an interval scale 38 4.1 Time-series plots of monthly regional unemployment in 1986 49 4.2 Time-series plots of East Anglian and North-Western unemployment in 1986 50 4.3 Histograms of regional unemployment in 1986 51 4.4 Alternative histogram of East Anglian unemployment in 1986 54 4.5 Stem-and-leaf plots of monthly unemployment