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Cross-Contamination in EI-R: Reply

  • Michael C. Herron (a1) and Kenneth W. Shotts (a2)

Extract

We address in Herron and Shotts (2003; hereinafter HS) an increasingly common statistical practice called EI-R, in which point estimates generated by the King (1997) ecological inference technique are used as dependent variables in second-stage linear regressions. Although HS argue that EI-R slope estimates are inconsistent and suffer from attenuation bias, this characterization of EI-R is excessively conservative. Indeed, we show here that EI-R estimates can suffer from sign reversals, attenuation bias, and augmentation bias, that inference based on these estimates can be misleading, and that EI-R is unfixable and should not be used.

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Adolph, Christopher, and King, Gary. 2003. “Analyzing Second-Stage Ecological Regressions: Comment on Herron and Shotts.” Political Analysis 11:6576.
Burden, Barry C., and Kimball, David C. 1998. “A New Approach to the Study of Ticket Splitting.” American Political Science Review 92:533544.
Burden, Barry C., and Kimball, David C. 2002. Why Americans Split Their Tickets: Campaigns, Competition, and Divided Government. Ann Arbor: The University of Michigan Press.
Gay, Claudine. 2001. “The Effect of Black Congressional Representation on Political Participation.” American Political Science Review 95:589602.
Herron, Michael C., and Shotts, Kenneth W. 2000a. “A Specification Test for Linear Regressions That Use King-Based Ecological Inference Point Estimates as Dependent Variables.” Paper presented at the Annual Meeting of the American Political Science Association, Washington, DC.
Herron, Michael C., and Shotts, Kenneth W. 2000b. “Using Ecological Inference Point Estimates in Second Stage Linear Regressions.” Paper presented at the Society for Political Methodology Summer Conference, Los Angeles.
Herron, Michael C., and Shotts, Kenneth W. 2002. “Logical Inconsistency in King-Based Ecological Regressions.” Paper presented at the Society for Political Methodology Summer Conference, Seattle, WA.
Herron, Michael C., and Shotts, Kenneth W. 2003. “Using Ecological Inference Point Estimates as Dependent Variables in Second-Stage Linear Regressions.” Political Analysis 11:4464.
King, Gary. 1997. A Solution to the Ecological Inference Problem. Princeton, NJ: Princeton University Press.
McCue, Kenneth F. 2001. “The Statistical Foundations of the EI Method.” The American Statistician 55(2): 106110.
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