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5 - On “Solutions” to the Ecological Inference Problem
- David A. Freedman
- Edited by David Collier, University of California, Berkeley, Jasjeet S. Sekhon, University of California, Berkeley, Philip B. Stark, University of California, Berkeley
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- Book:
- Statistical Models and Causal Inference
- Published online:
- 05 June 2012
- Print publication:
- 23 November 2009, pp 83-96
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- Chapter
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Summary
Abstract. In his 1997 book, King announced “A Solution to the Ecological Inference Problem.” King's method may be tested with data where truth is known. In the test data, his method produces results that are far from truth, and diagnostics are unreliable. Ecological regression makes estimates that are similar to King's, while the neighborhood model is more accurate. His announcement is premature.
Introduction
Before discussing King (1997), we explain the problem of “ecological inference.” Suppose, for instance, that in a certain precinct there are 500 registered voters of whom 100 are Hispanic and 400 are non-Hispanic. Suppose too that a Hispanic candidate gets ninety votes in this precinct. (Such data would be available from public records.) We would like to know how many of the votes for the Hispanic candidate came from the Hispanics. That is a typical ecological-inference problem. The secrecy of the ballot box prevents a direct solution, so indirect methods are used.
This review will compare three methods for making ecological inferences. First and easiest is the “neighborhood model.” This model makes its estimates by assuming that, within a precinct, ethnicity has no influence on voting behavior: In the example, of the ninety votes for the Hispanic candidate, 90 × 100/(100 + 400) = 18 are estimated to come from the Hispanic voters. The second method to consider is “ecological regression,” which requires data on many precincts (indexed by i).
6 - Rejoinder to King
- David A. Freedman
- Edited by David Collier, University of California, Berkeley, Jasjeet S. Sekhon, University of California, Berkeley, Philip B. Stark, University of California, Berkeley
-
- Book:
- Statistical Models and Causal Inference
- Published online:
- 05 June 2012
- Print publication:
- 23 November 2009, pp 97-104
-
- Chapter
- Export citation
-
Summary
Abstract. King's “solution” works with some data sets and fails with others. As a theoretical matter, inferring the behavior of subgroups from aggregate data is generally impossible: The relevant parameters are not identifiable. Unfortunately, King's diagnostics do not discriminate between probable successes and probable failures. Caution would seem to be in order.
Introduction
King (1997) proposed a method for ecological inference and made sweeping claims about its validity. According to King, his method provided realistic estimates of uncertainty, with diagnostics capable of detecting failures in assumptions. He also claimed that his method was robust, giving correct inferences even when the model is wrong.
Our review (Freedman, Klein, Ostland, and Roberts 1998 [Chapter 5]) showed that the claims were exaggerated. King's method works if its assumptions hold. If assumptions fail, estimates are unreliable: so are internally-generated estimates of uncertainty. His diagnostics do not distinguish between cases where his method works and where it fails. King (1999) raised various objections to our review. After summarizing the issues, we will respond to his main points and a few of the minor ones. The objections have little substance.
Model comparisons
Our review compared King's method to ecological regression and the neighborhood model. In our test data, the neighborhood model was the most accurate, while King's method was no better than ecological regression. To implement King's method, we used his software package EZIDOS, which we downloaded from his web site.
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