Bernard Grofman and Matt A. Barreto A Reply to Zax’s (2002) Critique of Grofman and Migalski (1988): Double-Equation Approaches to Ecological Inference When the Independent Variable Is Misspecified Sociological Methods & Research 2009 37: 599-617.
The authors reply to Zax’s critique of the double-equation method for ecological regression and of the specific extension to it proposed by Grofman and Migalski. Although Zax does correct two minor errors in Grofman and Migalski’s statement of the double-equation approach, neither of those errors affected the final calculations reported in their article. Furthermore, nothing Zax reports affects their fundamental conclusion that double-equation methods can be superior to single-equation techniques if there is substantial error in the measurement of the independent variable. In particular, by analyzing an election for which, from exit polls, the “true” parameters of Hispanic and non-Hispanic levels of political cohesion are known, the authors show that double-equation ecological regression estimates derived from registration data are highly accurate in reproducing the true individual-level behavioral parameters (group means).
Key Words: Elections • Voter Racial Turnout • Bloc Voting • Ecological Regression • Ecological Inference