Survey Sampling and Measurement Edited by N. KRISHNAN NAMBOODIRI DEPARTMENT OF SOCIOLOGY UNIVERSITY OF NORTH CAROLINA CHAPEL HILL, NORTH CAROLINA ACADEMIC PRESS New York San Francisco London 1978 A Subsidiary of Harcourt Brace Jovanovich, Publishers COPYRIGHT © 1978, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NW1 7DX Library of Congress Cataloging in Publication Data Symposium on Survey Sampling, 2d, University of North Carolina, 1977. Survey sampling and measurement. (Quantitative studies in social relations) Papers presented at the 2d Symposium on Survey Sampling held at the Chapel Hill campus of the University of North Carolina, Apr. 14-17,1977. Includes index. 1. Sampling (Statistics)—Congresses. 2. Social surveys—Congresses. I. Krishnan Namboodiri, N. II. Title. HA31.2.S97 1977 001.4'22 78-3345 ISBN 0-12-513350-2 PRINTED IN THE UNITED STATES OF AMERICA List of Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin. BARBARA A. BAILAR (69, 175), U.S. Bureau of the Census, Washing­ ton, D.C. 20233 LEROY BAILEY (175), U.S. Bureau of the Census, Washington, D.C. 20233 D. BASU (267, 337), Department of Statistics, The Florida State Uni­ versity, Tallahassee, Florida 32304 DWIGHT B. BROCK (121), Office of Statistical Research, National Center for Health Statistics, 3700 East-West Highway, Hyattsville, Maryland 20782 CAROL CORBY (175), Research Center for Measurement Methods, U.S. Bureau of the Census, Washington, D.C. 20233 WILLIAM G. CUMBERLAND (293, 331), Division of Biostatistics, School of Public Health, University of California, Los Angeles, Los Angeles, California 90024 xiii xiv List of Contributors ESTELA BEE DAGUM (217), Seasonal Adjustment and Time Series Analysis Staff, Statistics Canada, Tunney's Pasture, Ottawa, On tario, Canada K1A OT6 STEPHEN E. FIENBERG (89), Department of Applied Statistics, School of Statistics, University of Minnesota, St. Paul, Minnesota 55108 A. L. FINKNER* (45), U.S. Bureau of the Census, Washington, D.C. 20233 DANIEL H. FREEMAN, JR. (121), Department of Epidemiology and Public Health (Biometry), School of Medicine, Yale University, New Haven, Connecticut 06510 V. P. GODAMBE (311), Department of Statistics, University of Wa terloo, Waterloo, Ontario, Canada N2L 3G1 MORRIS H. HANSEN (341), Westat Corporation, Rockville, Maryland 20852 H. O. HARTLEY (35), Institute of Statistics, Texas A & M University, College Station, Texas 77843 D. G. HORVITZ (3), Statistical Sciences Group, Research Triangle Insti tute, P.O. Box 12194, Research Triangle Park, North Carolina 27709 LESLIE KISH (13), Survey Research Center, Institute for Social Re search, The University of Michigan, Ann Arbor, Michigan 48106 JAN KMENTA (107), Department of Economics, The University of Mi chigan, Ann Arbor, Michigan 48109 C. MICHAEL LANPHIER (69), Department of Sociology, York Univer sity, Downsview, Ontario, Canada M3J 1P3 WILLIAM G. MADOW (315, 341), 700 New Hampshire Avenue N.W., Washington, D.C. 20037 M. N. MURTHY (231), Statistical Institute for Asia and the Pacific, P.O. Box 13, Akasaka, Tokyo 107, Japan HAROLD NISSELSON (45), U.S. Bureau of the Census, Washington, D.C. 20233 R. PLATEK (157), Household Surveys Development Division, Statistics Canada, R. H. Coats Building, Tunney's Pasture, Ottawa, Ontario, Canada K1A OT6 J. N. K. RAO (35, 323), Department of Mathematics, Arts Tower, Carleton University, Ottawa, Ontario, Canada K1S 5B6 * Present address: Research Triangle Institute, Research Triangle Park, North Carolina 27709. List of Contributors XV RICHARD M. ROYALL (293, 331), Department of Biostatistics, School of Hygiene and Public Health, The Johns Hopkins University, Balti­ more, Maryland 21205 J. SEDRANSK (143), Statistical Science Division, State University of New York at Buffalo, Buffalo, New York 14214 B. V. SHAH (25), Statistical Sciences Group, Research Triangle Insti­ tute, P.O. Box 12194, Research Triangle Park, North Carolina 27709 BAHADUR SINGH* (143), National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709 M. P. SINGH (157), Statistics Canada, Tunney's Pasture, Ottawa, On­ tario, Canada K1A OT6 T. M. F. SMITH (201), Department of Mathematics, University of Southampton, Southampton, England S09 5NH V. TREMBLAY (157), Centre de Sondage, Université de Montréal, C.P. 6128, Montréal, Québec, Canada P. VUAGNAT (255), Mathematics Section, University of Geneva, 11211 Geneva 24 Switzerland * Present address: Department of Statistics, State University of New York at Buffalo, Buffalo, New York 14214. Preface It is well known that when survey sampling was in its infancy, most theorists were practitioners and most practitioners were theorists. Problems encountered in practice fostered theory, and advances in theory nurtured practice. This happy state of affairs does not seem to exist now. Today, sampling theorists do not engage in conducting surveys, and prac­ titioners ignore the new theoretical exhortations. Can anything be done to bring theory and practice together again? If there has occurred a separation between theory and practice, a simi­ lar gap has opened up between "survey objectives" and "survey data use." It is well recognized that even today sample surveys are largely enumerative and descriptive in their objectives—to estimate a number of totals, scores of proportions, and myriads of means. But once the initially proclaimed objectives of the survey are met, the data are often made available for public use, mostly through data banks. And in the hands of John Q. Public, who is interested in analytic studies, survey data are, irre­ spective of the complexity of the sample design involved, a random sample from an infinite population characterized by a convenient proba- xvii xviii Preface bility distribution. Multivariate models such as path models are fitted to the data under such assumptions, and these models are then used in criti cizing or formulating public policies, in revising or constructing substan tive theories, in assessing changes, in forecasting the future, and for simi lar mundane purposes. Is it legitimate to superimpose on sample survey data convenient stochastic models? Is it safe to ignore the sample design at the analysis stage? With questions like these uppermost in our minds, four of us (A. Beza, N. L. Johnson, N. K. Namboodiri, and H. B. Wells) at the Chapel Hill campus of the University of North Carolina approached the National Sci ence Foundation in 1976 with a request for financial support for a sympo sium on survey sampling and measurement. Our request was granted, and the symposium was held at Chapel Hill in April 1977. It was the Second Symposium on Survey Sampling (SSSS), the first one having been the in ternational Symposium on the Foundations of Survey Sampling held on the campus in 1968. This volume contains the invited papers presented at the 1977 sympo sium. No attempt was made to record the informal discussions that took place following the presentations; the authors were, however, encouraged to revise their papers in light of the comments from the participants. Formal discussion was organized only in one session, in which D. Basu presented a paper on the relevance of randomization in data analysis and R. M. Royall and W. G. Cumberland delivered one on an empirical study of prediction theory in finite population sampling. These papers were dis cussed by V. P. Godambe, W. G. Madow, and J. N. K. Rao. After the symposium, the written versions of the discussants' comments were made available to the authors for their reactions. The comments and the authors' rejoinders are included in this volume. The volume is divided into seven parts. In Part I, D. G. Horvitz, with an eye toward improving the quality of sample surveys, makes a plea for the creation of a computerized system of information on error estimates associated with the design and execution of surveys, and L. Kish suggests a realistic agenda for future work in survey sampling practice and theory. Part II contains four papers, each dealing with specific methodological problems. B. V. Shah advocates the use of the linear term in the Taylor expansion to obtain approximate expression for the variance. H. O. Hartley and J. N. K. Rao suggest a method for estimating the overall (sampling plus nonsampling) variance of linear estimators in surveys based on stratified multistage designs with equal-probability selection at the last stage. A. L. Finkner and H. Nisselson discuss, on the basis of the experience at the U.S. Bureau of the Census, several problems associated with continuing cross-section surveys. C. M. Lanphier and B. A. Bailar Preface XIX describe special sampling-frame problems that were encountered in a study of appropriate design strategies for a survey of surveys in the United States. Part HI contains three papers, each dealing with selected problems of analysis of survey data. S. E. Fienberg reviews the design and execution of the National Crime Survey and describes some stochastic models that may be used in the analysis of the data from that source. He takes the po sition that "it is unclear whether we need to take into account the com plexities of the sample design when we try to model the victimization his tories of individuals with common sociodemographic and geographic characteristics." J. Kmenta discusses survey data analysis from an econ- ometrician's standpoint; he gives particular attention to problems such as how to formulate and test simultaneous equation models using cross- sectional data. D. H. Freeman and D. B. Brock demonstrate, with data from health surveys in the United States, that in the analysis of complex survey data the use of appropriately estimated covariance matrices is rewarding, because when they are used in the analysis it becomes pos sible to detect nonzero differences between domain estimates, which may otherwise go undetected. The chapters in Part IV deal with nonresponse, undercoverage, and re lated problems. B. Singh and J. Sedransk consider, from a Bayesian view point, inferences concerning the mean of a finite population, under a two-phase sampling scheme with post-stratification, and analyze as a spe cial case of this general approach the problem of nonresponse in surveys. R. Platek, M. P. Singh, and V. Tremblay use the concept of response probabilities to develop response-nonresponse error components under various commonly used methods for adjusting for nonresponse. B. A. Bailar, L. Bailey, and C. Corby describe adjustment procedures devel oped at the U.S. Bureau of the Census to handle nonresponse, undercov erage, and the like. Part V contains two papers, both dealing with time series analysis. T. M. F. Smith examines the application of classical time series models of the autoregressive integrated moving average (AIMA) type to data from repeated surveys. E. B. Dagum discusses a method developed at Statistics Canada for estimating changes in seasonal variations in eco nomic time series such as monthly data on labor force. In Part VI, chapters by M. N. Murthy and P. Vuagnat deal with what may be called applications of sample survey data and methods. Murthy points out that the state of affairs with respect to the availability of reli able data for use in national planning in developing countries is indeed alarming. He then suggests ways to improve the situation. Vuagnat dis cusses the problems in the application of sampling methods in geology. XX Preface Part VII deals with the gap between current survey practices and recent theoretical developments. D. Basu expounds the eyebrow-raising thesis that "at the analysis stage, we have no need to concern ourselves with the exact nature of the [sample] design. . . ." R. M. Royall and W. G. Cum­ berland supply empirical material relevant to their claim that "analysis based on prediction models and directed to specific samples can reveal re­ lationships which are essential in making inferences, but which are con­ cealed in analyses which entail averaging over all possible samples." The comments on these two chapters and the rejoinders reveal that theorists themselves are not in agreement with each other on many crucial issues. In the final chapter, M. H. Hansen and W. G. Madow review the efforts of theorists to replace the "conventional survey practice," namely the prob­ ability sampling approach, with the framework of traditional statistical theory, in which models and distributions are assumed, and analysis is guided by these assumptions. The Hansen-Madow position is that in large-scale sample surveys the essentially assumption-free approach of "the conventional sampling practice" has substantial advantages over its suggested alternative, since the objective of such surveys is to obtain rela­ tively high precision in inferences concerning finite, highly heterogenous populations. They concede, however, that when the aim is to make infer­ ences about causal systems, model-based approaches do have a role to play. Many interesting topics receive little or no attention herein. For this, the subjective sampling plan adopted by the symposium organizers is to blame. It is hoped that this volume will be of interest to survey statisticians as well as to survey data users. If it stimulates thoughtful and courageous attack on some of the unresolved problems in survey sampling, its mission will have been amply fulfilled. ACKNOWLEDGMENTS The symposium was sponsored by the Institute for Research in Social Science, and the Departments of Statistics, Sociology, and Biostatistics, University of North Carolina at Chapel Hill. The sponsors are grateful to the National Science Foundation for its generous grant (Grant Number Soc 76-23208) which made the symposium possible. The sponsors are also grateful to the authors for their careful prepara­ tion of the chapters. The views expressed are, however, those of the authors and not necessarily those of the sponsors or of the National Science Foundation. Preface xxi Local arrangements were made by W. H. Heriford and his staff at the Extension division of the University of North Carolina at Chapel Hill. O. A. Andrew of the Department of Sociology unstintingly contributed her time and talent to help with the organization, to assist the participants in all possible ways, and in several other tangible and intangible respects. S. Morton served as symposium secretary. The sponsors are thankful to these persons and to Vice Chancellor Lyle V. Jones who took time out from his busy schedule to welcome the participants. Thanks are also due to those who served as session chairmen: R. J. Carroll, J. Grizzle, D. M. Hawkins, N. K. Namboodiri, W. G. Cocharan, M. Francis, J. Murphy, G. Simmons, G. Koch, J. Sedransk, S. L. Stokes, H. B. Wells, and A. Beza. Finally the writer of these lines, in his capacity as the symposium chairman, wishes to express his appreciation to A. Beza for his assistance in drafting the proposal to the National Science Foundation, and to the three cochairmen of the symposium (A. Beza, N. L. Johnson, and H. B. Wells) for their invaluable contributions in developing the program and selecting the speakers and participants. N.K.N.