Spatial Choices and Processes PDF
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Studies in Regional Science and Urban Economics Series Editors ΑKE E. ANDERSON WALTER ISARD PETER NIJKAMP Volume 21 NORTH-HOLLAND - AMSTERDAM · NEW YORK» OXFORD» TOKYO Spatial Choices and i*rocesses Editors MANFRED M. FISCHER Department of Economic and Social Geography Vienna University of Economics and Business Administration Vienna, Austria PETER NIJKAMP Department of Economics Free University Amsterdam, The Netherlands YORGOS Y. PAPAGEORGIOU Department of Geography McMaster University, Hamilton Ontario, Canada 1990 NORTH-HOLLAND - AMSTERDAM · NEW YORK · OXFORD · TOKYO ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 RO. Box 211, 1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 655 Avenue of the Americas New York, N.Y 10010, U.S.A. Library of Congress Cataloging-in-Publicat¡on Data Spatial choices and processes / editors, Manfred M. Fischer, Peter Nijkamp, Yorgos Y. Papageorgiou. p. cm. - (Studies in regional science and urban economics ; v. 21) "Originated from a symposium organised under the auspices of the IGU Working Group on Mathematical Models which was held in Canberra, in August 1988." Includes bibliographical references and index. ISBN 0-444-88195-6 1. Urban economics - Mathematical models - Congresses. 2. Spatial behavior - Mathematical models - Congresses. I. Fischer, Manfred M., 1947- II. Nijkamp, Peter. III. Papageorgiou, Y.Y. IV. IGU Working Group on Mathematical Models. V. Series. HT321.S67 1990 330.9173'2-dc20 90-47849 CIP ISBN: 0 444 88195 6 © ELSEVIER SCIENCE PUBLISHERS B.V., 1990 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Physical Sciences and Engineering Division, PO. Box 1991, 1000 BZ Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about condi tions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science Publishers B.V., unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instruc tions or ideas contained in the material herein. p.p. 293-312: Copyright not transferred. Printed in The Netherlands PREFACE Today, the field of behavioural modelling is a more or less established field with educational and research programmes at many universities. It is a field in which researchers may rely on specific facets, disciplines and methodologies. The piecemeal publication of new research in this field and a wide range of psychological, economic, geographic, regional science and statistical journals, however, make it difficult for scholars not actively working in this interdisciplinary field to overview the existing state of knowledge and the present frontiers of research. The present volume attempts to illustrate some recent developments in the field of behavioural modeUing of spatial decisions and processes and aims to disseminate recent research into the graduate classrooms. It originated from a symposium organised under the auspices of the IGU Working Group on Mathematical Models which was held in Canberra in August 1988. We would like to thank the chairs of this IGU Working Group, Professor MacKinnon and Hubert Beguin, for their support. The present volume includes a selection of contributions to this symposium comple mented with some solicited additional papers. In the field of spatial choice and process modelling a leading role has been played by our late colleague, Georgio Leonardi, who has paved so much of the road toward a thorough scientific analysis of the behaviour of actors in space. We are very grateful for all his efforts and excellent scholarship and we are happy to dedicate this volume to him. In producing the book, we have profited by friendship and pressed colleagues for advice and assistance in the form of referee reports. Their willingness to help and the soundness of their comments and ideas have contributed immensely to the quality of this volume. We would like to acknowledge also the timely manner in which most of the contributing authors responded to all our requests. Moreover, the cartographic support provided by the Department of Geography of the University of Vienna has to be acknowledged. Finally, we appreciate the editorial assistance given by Dianne Biederberg. Vienna May 1990 Manfred M. Fischer Amsterdam Peter Nijkamp Hamilton Yorgos Y. Papageorgiou xiii FIGURES Page 2.1 Different Classes of Dynamic Choice Modelling Approaches 18 2.2 The Master Equation Point of View: The Relationship between the Micro- and Macro-Level in Decision Processes 26 2.3 The Relationship between Innovation Diffusion and Individual Choice: The Duality Point of View 33 3.1 Bifurcation Diagrams of a May-Logistic Map (2.9<a<3.9) 53 3.2 The Hιnon Attractor 54 3.3 The Chaotic Region for Gilpin's Equations: (a) A4-Cycle, (b) A4-Cycle plus Complex Behaviour 56 3.4 Projection of the Lorenz-Attractor for r=28, b=3/8 and σ= 10 57 3.5 The Rφssler Attractor. Three-Dimensional Views with a=0.343, b = 1.82 and c=9.75: The Axes Form a Cube which has been Rotated around the y-Axis (see (a) and (b)) and z-Axis (see (c) and (d)) 58 3.6 Modest Urban Decline 66 3.7 Chaotic Urban Decline 67 4.1 Determination of the Constants c^ 85 6.1 Mixing Distributions for Different Household Types 128 6.2 Patterns of Heterogeneity for a Single Choice Alternative from a Four Alternative Dirichlet-Logistic Model 132 6.3 Predicted Patterns of Heterogeneity for a Single Choice Alternative from a 3-Mass-Points and Dirichlet-Logistic Model 139 7.1 Map of Activity Space Elements, Actual and Estimated Sample Locations for Subject 64 158 7.2 Map of Activity Space Elements, Actual and Estimated Sample Locations for Subject 100 158 7.3 Error Ellipses for All Minor Nodes 159 7.4 Error Ellipses for Best Known Places 159 8.1 A Conceptual Representation of NAVIGATOR 175 8.2 Changing Representation in the LTM at the End of Two Simulations 197 10.1 Income Expansion Paths 231 10.2 G(X) Mapping 231 10.3 Market Clearing Price Functions 231 xiv Page 10.4 Distribution of Estimated Mean Willingness to Pay. Income Elasticity of Expenditure on X < 1: (a) Small Error Size, (b) Medium Error Size, (c) Larger Error Size 235 10.5 Distribution of Estimated Mean Willingness to Pay. Income Elasticity of Expenditure on X > 1: (a) Small Error Size, (b) Medium Error Size, (c) Larger Error Size 236 10.6 Distribution of Estimated Mean Willingness to Pay. Income Elasticity of Expenditure on X = 1: (a) Small Error Size, (b) Medium Error Size, (c) Larger Error Size 237 14.1 Internal Pool Adjustments 294 15.1 A Decision Tree for Work Location and Residential Choice 316 16.1 Graphic Presentations of the Functional Form of the Composite Scores 336 17.1 Tree Structure of the PRC Process whereby the Passenger's Route Choice r^, to any Destination, dj, is Preceded by the Choice of Departure Airport, aj 351 17.2 Tree Structure of the PRC Process whereby the Route Type is Initially Selected Followed by the Choice of Hub Location and then Departure Aiφort 351 XV TABLES Page 6.1 Parameter Estimates of Local/Non-Local Shopping Centre Choice Model 126 6.2 Characteristics of Mixing Distributions for the Shopping Centre Choice Model 127 6.3 Expected Probabilities of Choosing Different Shopping Alternatives for Three Types of Household 134 6.4 Expected Probabilities of Choosing Different Shopping Alternatives for Four Types of Household 140 7.1 Comparison Distortion and Error Associated with Anchor Points (Best Known Cues) and Lesser Known Places 157 8.1 Parameter-Set Interactions 182 8.2 Analysis of Simulations: 185 (a) Saliency Values of Selected Decision Points over Repeated Simulations (b) Effects of Route Complexity of Output Measures 8.3 Analysis of Simulation 190 8.4 Comparison of the Two Search Procedures 195 9.1 Logit and Probit Covariance Matrices 207 9.2 Estimation Results of Logit Models 211 9.3 Estimation Results of Probit Models 213 10.1 Utility Functions and Initial Conditions 228 10.2 Percentage of Observations in which the Identity of the Utility Maximising Alternative is Changed by Including a Stochastic Error 228 10.3 Mean Values of Parameter Estimates 229 10.4 Mean Correlation Coefficient between True and Estimated Utility Levels ( δ =1) 230 10.5 Per Cent of Consumer Choices Correctly Predicted 230 10.6 True and Estimated Average Willingness to Pay for Marginal Unit of χ 234 10.7 Average Correlation Coefficient between True and Estimated Willingness to Pay 238 10.A1 Average Value of Intercept of Regression of True Willingness to Pay on Estimated Value 241 10. A2 Average Value of Slope Regression of True Willingness to Pay on Estimated Value 242 XVI Page 11.1 Variables of the College Choice Models 259 12.1 Alternative Stated Response Emphases 266 12.2 The First Stage Design 270 12.3 A Double-Conditional (Main Effects) Choice Design 272 12.4 The Empirical Implications of Approach I 273 12.5 The Empirical Implications of Approach I with Pooled Data and Equal Choice Proportions 274 12.6 The Empirical Implications of Approach II 275 15.1 The Degree of Displacement: Estimation Results for Choice 2 324 15.2 Overview of the Quality and Feedback Structure of the Submodels 326 16.1 Simple Choices for Scores 337 16.2 Normalised Orthogonal Polynomial Scores for Three and Four Category Variables 337 16.3 Kronecker Product of K^ and Kg 339 16.4 Models for Single Persons Owner-Occupier Households 341 16.5 Model for Single Person Owner-Occupier Households 341 16.6 Coefficients for Models 1 through 8 344 16.7 Parameter Values for the Empirical Example 345 16.8 Calculations of Log-Odds of Choice 346 17.1 Explanatory Variables Used in Initial Models Specification Search 356 17.2 Coefficient Estimates for MNL Models 358 17.3 Coefficient Estimates for NMNL Models 361 17.4 Prediction of Passenger Route Choice for Various Destinations 362 17.5 Summary Statistics for PRC Model Prediction by Destination 363 xvii CONTRIBUTING AUTHORS Peter O. Barnard Gerard H.M. Evers School of Economics Department of Economics MacQuarie University and Australian Catholic University Brabant Road Research Board PO Box 90153 Sydney NL-5000 LE Tilburg New South Wales 2109 The Netherlands Australia Manfred M. Fischer Axel Bφrsch-Supan Department of Economic and Department of Economics Social Geography University of Mannheim Vienna University of Economics and Postfach 10 34 62 Business Administration D-6800 Mannheim Augasse 2-6 Federal Republic of Germany A-1090 Vienna Austria Robert Caves Department of Transport Technology Reginald Golledge University of Technology Department of Geography Loughborough University of California Leicestershire LEll 3TU Santa Barbara, CA 93106 United Kingdom USA William A.V. Clark Sucharita Gopal Department of Geography Department of Geography University of California at Los Angeles Boston University 1255 Bunche Hall 675 Commonwealth Avenue Los Angeles, CA 90024 Boston, MA 02215 USA USA Marinus C. Deurloo Gόnter Haag Department of Geography Department of Theoretical Physics University of Amsterdam University of Stuttgart Jodenbreestraat 23 Pfaffenwaldring 57 Amsterdam D-7000 Stuttgart 80 The Netherlands Federal Republic of Germany Frans Μ. Dieleman David A. Hensher Department of Geography School of Economic and State University of Utrecht Financial Studies PO Box 80115 MacQuarie University NL-3508 TC Utrecht Sydney The Netherlands New South Wales 2109 Australia xvm Joel L Horowitz Yorgos Y. Papageorgiou Departments of Geography and Department of Geography Economics McMaster University University of Iowa 1280 Main Street West Iowa City, lA 52240 Hamilton, Ontario L8S 4U1 USA Canada Lester W. Johnson Yannis Papageorgiou School of Business Department of Mathematics Bond University Yale University Gold Coast New Haven, Connecticut Queensland 4229 USA Australia David Pitfield Georgio Leonardi Department of Transport Technology University of Technology Jordan L. Louviere Loughborough Department of Marketing and Leicestershire LEll 3TU Economic Analysis United Kingdom University of Alberta Edmonton, Alberta T6E 2R6 John M. Quigley Canada Graduate School of Public Policy University of California Carl Mason Berkeley Graduate School of Public Policy 2607 Hearst Avenue University of California Berkeley, CA 94720 Berkeley USA 2607 Hearst Avenue Berkeley, CA 94720 Aura Reggiani USA Department of Mathematics University of Bergamo Ngoe Ndoh Via Salvecchio 19 Department of Transport Technology Bergamo University of Technology Italy Loughborough Leicestershire LEll 3TU John R. Roy United Kingdom CSIRO Division of Building, Construction and Peter Nijkamp Engineering Department of Economics Graham Road Free University Highett, Victoria 3190 De Boelelaan 1105 Australia NL·1081 HV Amsterdam The Netherlands
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