Monte Carlo Simulation Sage University title: Papers Series. Quantitative Applications in the Social Sciences ; No. 07-116 author: Mooney, Christopher Z. publisher: Sage Publications, Inc. isbn10 | asin: 0803959435 print isbn13: 9780803959439 ebook isbn13: 9780585213323 language: English subject Monte Carlo method. publication date: 1997 lcc: QA298.M66 1997eb ddc: 519.2/82 subject: Monte Carlo method. Monte Carlo Simulation SAGE UNIVERSITY PAPERS Series: Quantitative Applications in the Social Sciences Series Editor: Michael S. Lewis-Beck, University of Iowa Editorial Consultants Richard A. Berk, Sociology, University of California, Los Angeles William D. Berry, Political Science, Florida State University Kenneth A. Bollen, Sociology, University of North Carolina, Chapel Hill Linda B. Bourque, Public Health, University of California, Los Angeles Jacques A. Hagenaars, Social Sciences, Tilburg University Sally Jackson, Communications, University of Arizona Richard M. Jaeger, Education, University of North Carolina, Greensboro Gary King, Department of Government, Harvard University Roger E. Kirk, Psychology, Baylor University Helena Chmura Kraemer, Psychiatry and Behavioral Sciences, Stanford University Peter Marsden, Sociology, Harvard University Helmut Norpoth, Political Science, SUNY, Stony Brook Frank L. Schmidt, Management and Organization, University of Iowa Herbert Weisberg, Political Science, The Ohio State University Publisher Sara Miller McCune, Sage Publications, Inc. INSTRUCTIONS TO POTENTIAL CONTRIBUTORS For guidelines on submission of a monograph proposal to this series, please write Michael S. Lewis-Beck, Editor Sage QASS Series Department of Political Science University of Iowa Iowa City, IA 52242 Page i Series/Number 07-116 Monte Carlo Simulation Christopher Z. Mooney West Virginia University SAGE PUBLICATIONS International Educational and Professional Publisher Thousand Oaks London New Delhi Copyright © 1997 by Sage Publications, Inc. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. For information address: SAGE Publications, Inc. 2455 Teller Road Thousand Oaks, California 91320 E-mail: [email protected] SAGE Publications Ltd. 6 Bonhill Street London EC2A 4PU United Kingdom SAGE Publications India Pvt. Ltd. M-32 Market Greater Kailash I New Delhi 110 048 India Printed in the United States of America Library of Congress Cataloging-in-Publication Data Mooney, Christopher Z. Monte Carlo simulation / author, Christopher Z. Mooney. p. cm. (Quantitative applications in the social sciences ;Vol. #116) Includes bibliographical references (p. ). ISBN 0-8039-5943-5 (pbk.) 1. Monte Carlo method. I. Title. II. Series: Sage university papers series. Quantitative applications in the social sciences ; no. 116. QA298.M66 1997 519.2'82dc21 96- 45873 CIP 99 00 01 02 03 10 9 8 7 6 5 4 3 2 Acquiring Editor: C. Deborah Laughton Editorial Assistant: Eileen Carr Production Editor: Sherrise M. Purdum Production Assistant: Denise Santoyo Typesetter/Designer: Andrea D. Swanson When citing a university paper, please use the proper form. Remember to cite the current Sage University Paper series title and include the paper number. One of the following formats can be adapted (depending on the style manual used): (1) Mooney, C. Z. (1997) Monte Carlo Simulation. Sage University Paper series on Quantitative Applications in the Social Sciences, 07-116. Thousand Oaks, CA: Sage. OR (2) Mooney, C. Z. (1997) Monte Carlo Simulation (Sage University Paper series on Quantitative Applications in the Social Sciences, series no.07-116). Thousand Oaks, CA: Sage. Page iii Contents Acknowledgments v Series Editor's Introduction vii 1. Introduction 1 1.1 The Monte Carlo Principle 3 2. Generating Individual Samples From a Pseudo- 5 Population 2.1 Setting Up a Population Generating Computer 5 Algorithm 2.2 Generating Single Random Variables 7 2.3 Generating Combinations of Random Variables 42 3. Using the Pseudo-Population in Monte Carlo Simulation 50 3.1 An Example of a Complete Pseudo-Population 50 Algorithm 3.2 Generating a Vector of Monte Carlo Estimates 52 3.3 Generating Multiple Experiments 55 3.4 Which Statistic Is to Be Saved From a Trial? 56 3.5 How Many Trials Are Needed? 57 3.6 Evaluating Monte Carlo Estimates of Sampling 59 Distributions 4. Using Monte Carlo Simulation in the Social Sciences 65 4.1 Inference When Weak Statistical Theory Exists for 66 an Estimator 4.2 Testing a Null Hypothesis Under a Variety of 72 Plausible Conditions 4.3 Assessing the Quality of an Inference Method 77 4.4 Assessing the Robustness of Parametric Inference to 82 Assumption Violations 4.5 Comparing Estimators' Properties 88 Page iv 5. Conclusion 92 Notes 97 References 99 About the Author 103