Analyzing Second-Stage Ecological Regressions: Comment on Herron and Shotts

Author:

Adolph Christopher,King Gary

Abstract

We take this opportunity to comment on Herron and Shotts (2003; hereinafter HS) because of its interesting and productive ideas and because of the potential to affect the way a considerable body of practical research is conducted. This article, and the literature referenced therein, is based on the suggestions in three paragraphs in King (1997, pp. 289–290). Because these paragraphs were not summarized in HS, we thought they might be a useful place to start.

Publisher

Cambridge University Press (CUP)

Subject

Political Science and International Relations,Sociology and Political Science

Reference12 articles.

1. Imai Kosuke , and King Gary . 2002. “Did Illegally Counted Overseas Absentee Ballots Decide the 2000 U.S. Presidential Election?” (Available from http://gking.harvard.edu/preprints.shtml#ballots.)

2. An Alternative to Ecological Correlation

3. Multiple-Imputation Inferences with Uncongenial Sources of Input

4. Our notation deviates from HS only to ensure logical consistency. For example, their Eqs. (7) and (8) have different dependent variables, set equal to the same entire right side of the equation in both cases (α + γ'Zi + vi ). Later in their paper, they allow γ to differ between the two (calling the first γR and the second γU ), but do not change the constant term (or error terms). We fix these issues and others.

5. Indeed, after we finished a draft, Herron and Shotts told us that they had the same constant correction in a draft version of their paper, but took it out in the final version to save space. Because HS suggest correcting the slope, Comment on Herron and Shotts and do not mention constant term corrections, when we refer to the HS partially adjusted procedure, we are referring to what readers would conclude that Herron and Shotts advocate, even though we now know (from our subsequent correspondence) that they also believe the corrections discussed in their paper are incomplete for real applications.

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