A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data - Softcover

King, Gary

 
9780691012407: A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data
Softcover
ISBN 10: 0691012407 ISBN 13: 9780691012407
Verlag: Princeton University Press, 1997

Inhaltsangabe

This book provides a solution to the ecological inference problem, which has plagued users of statistical methods for over seventy-five years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? In political science, this question arises when individual-level surveys are unavailable (for instance, local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). This ecological inference problem also confronts researchers in numerous areas of major significance in public policy, and other academic disciplines, ranging from epidemiology and marketing to sociology and quantitative history. Although many have attempted to make such cross-level inferences, scholars agree that all existing methods yield very inaccurate conclusions about the world. In this volume, Gary King lays out a unique--and reliable--solution to this venerable problem.


King begins with a qualitative overview, readable even by those without a statistical background. He then unifies the apparently diverse findings in the methodological literature, so that only one aggregation problem remains to be solved. He then presents his solution, as well as empirical evaluations of the solution that include over 16,000 comparisons of his estimates from real aggregate data to the known individual-level answer. The method works in practice.


King's solution to the ecological inference problem will enable empirical researchers to investigate substantive questions that have heretofore proved unanswerable, and move forward fields of inquiry in which progress has been stifled by this problem.

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Über die Autorin bzw. den Autor

Gary King is Professor of Government at Harvard University. He has authored and coauthored numerous journal articles and books in the field of political methodology, including Designing Social Inquiry: Scientific Inference in Qualitative Research (Princeton).

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"This is a significant contribution to political methodology, and to statistical methodology throughout the social sciences. As always with Gary King's work, it is written with great flair and sophistication. This book will generate a good deal of excitement at the methodological frontier, and will also have a bracing impact on substantive research in a variety of fields."--Larry M. Bartels, Princeton University

"In this work, Gary King presents a number of new and important contributions to the field of statistical theory, and the practice of estimating choice probabilities from data aggregated into groups. An impressive statistical contribution."--Melvin J. Hinich, University of Texas-Austin

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A Solution to the Ecological Inference Problem

RECONSTRUCTING INDIVIDUAL BEHAVIOR FROM AGGREGATE DATA

By Gary King

PRINCETON UNIVERSITY PRESS

Copyright © 1997 Princeton University Press
All rights reserved.
ISBN: 978-0-691-01240-7

Contents

List of Figures............................................................xi
List of Tables.............................................................xiii
Preface....................................................................xv
Part I: Introduction.......................................................l
1 Qualitative Overview.....................................................3
2 Formal Statement of the Problem..........................................28
Part II: Catalog of Problems to Fix........................................35
3 Aggregation Problems.....................................................37
4 Non-Aggregation Problems.................................................56
Part III: The Proposed Solution............................................75
5 The Data: Generalizing the Method of Bounds..............................77
6 The Model................................................................91
7 Preliminary Estimation...................................................123
8 Calculating Quantities of Interest.......................................141
9 Model Extensions.........................................................158
Part IV: Verification......................................................197
10 A Typical Application Described in Detail: Voter Registration by Race...199
11 Robustness to Aggregation Bias: Poverty Status by Sex...................217
12 Estimation without Information: Black Registration in Kentucky..........226
13 Classic Ecological Inferences...........................................235
Part V: Generalizations and Concluding Suggestions.........................247
14 Non-Ecological Aggregation Problems.....................................249
15 Ecological Inference in Larger Tables...................................263
16 A Concluding Checklist..................................................277
Part VI: Appendices........................................................293
A Proof That All Discrepancies Are Equivalent..............................295
B Parameter Bounds.........................................................301
C Conditional Posterior Distribution.......................................304
D The Likelihood Function..................................................307
E The Details of Nonparametric Estimation..................................309
F Computational Issues.....................................................311
Glossary of Symbols........................................................313
References.................................................................317
Index......................................................................337


CHAPTER 1

Qualitative Overview


Political scientists have understood the ecological inference problemat least since William Ogburn and Inez Goltra (1919) introducedit in the very first multivariate statistical analysis of politics publishedin a political science journal (see Gow, 1985; Bulmer, 1984). In a studyof the voting behavior of newly enfranchised women in Oregon, theywrote that "even though the method of voting makes it impossibleto count women's votes, one wonders if there is not some indirectmethod of solving the problem. The height of a waterfall is not measuredby dropping a line from the top to the bottom, nor is the distancefrom the earth to the sun measured by a rod and chain" (p. 414).

Ogburn and Goltra's "indirect" method of estimating women'svotes was to correlate the percent of women voting in each precinctin Portland, Oregon, with the percent of people voting "no" in selectedreferenda in the same precincts. They reasoned that individualwomen were probably casting ballots against the referenda questionsat a higher rate than men "if precincts with large percentages ofwomen voting, vote in larger percentages against a measure than theprecincts with small percentages of women voting." But they (correctly)worried that what has come to be known as the ecologicalinference problem might invalidate their analysis: "It is also theoreticallypossible to gerrymander the precincts in such a way that theremay be a negative correlative even though men and women each distributetheir votes 50 to 50 on a given measure" (p. 415). The essenceof the ecological inference problem is that the true individual-levelrelationship could even be the reverse of the observed aggregate correlationif it were the men in the heavily female precincts who voteddisproportionately against the referenda.

Ogburn and Goltra's data no longer appear to be available, but theproblem they raised can be illustrated by this simple hypothetical examplereconstructed in part from their verbal descriptions. Considertwo equal-sized precincts voting on Proposition 22, an initiative bythe radical "People's Power League" to institute proportional representationin Oregon's Legislative Assembly elections: 40% of votersin precinct 1 are women and 40% of all voters in this precinct opposethe referenda. In precinct 2, 60% of voters are women and 60%of the precinct opposes the referenda. Precinct 2 has more womenand is more opposed to the referenda than precinct 1, and so it certainlyseems that women are opposing the proportional representationreform. Indeed, it could be the case that all women were opposedand all men voted in favor in both precincts, as might have occuredif the reform were uniformly seen as a way of ensuring men a placein the legislature even though they formed a (slight) minority in everylegislative district. But however intuitive this inference may appear,simple arithmetic indicates that it would be equally consistentwith the observed aggregate data for men to have opposed proportionalrepresentation at a rate four times higher than that of women.These higher relative rates of individual male opposition would occur,given the same aggregate percentages, if a larger fraction of menin the female-dominated precinct 2 opposed the reform than men inprecinct 1, as might happen if precinct 2 was a generally more radicalarea independent of, or even because of, its gender composition.

But if Ogburn and Goltra were Leif Ericson, William Robinson wasChristopher Columbus: for not until Robinson's (1950) article was theproblem widely recognized and the quest for a valid method of makingecological inferences begun in earnest. Robinson's article remainsone of the most influential works in social science methodology. His(correct) view was that, with the methods available at the time, validecological...

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Verlag
Princeton University Press
Erscheinungsdatum
1997
Sprache
Englisch
ISBN 10 
0691012407
ISBN 13 
9780691012407
Einband
Taschenbuch
Anzahl der Seiten
364
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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