Most existing models of ecological inference are based on the assumption that there is no aggregation bias. Few studies have focused on how to correct/ model aggregation bias. This article takes advantage of a unique opportunity to compare the controversial ecological inference methods by using aggregate as well as individual-level data from an actual election. Furthermore, the true quantities of interest are also available, which guarantees the accuracy of the empirical tests. Our mean squared error analyses show that King's Ecological Inference (EI) basic model does not always outperform the traditional ecological regression and neighborhood methods when aggregation bias does exist. However, using an appropriate covariate in the King's EI extended model to correct the aggregation bias problem can drastically improve the estimation accuracy at both the precinct and district levels. This article also makes suggestions on how to use a covariate in a King's extended model.
Achen, Christopher H. and W. Phillips Shively .1995. Cross-Level Inference. Chicago: University of Chicago Press.
2.
Adolph, Christopher, Gary King, Michael C. Herron, and Kenneth W. Shotts .2003. ``A Consensus on Second Stage Analysis in Ecological Inference Models.'' PoliticalAnalysis11:86-94.
3.
Anselin, Luc and Wendy K.Tam Cho.2002. ``Spatial Effects and Ecological Inference.'' Political Analysis10:276-97.
4.
Browning, Rufus P., Dale Rogers Marshall, and David H. Tabb.2003. Racial Politics in American Cities. New York: Longman Publishers.
5.
Burden, Barry C. and David C. Kimball .1998. ``A New Approach to the Study of Ticket Splitting.'' American Political Science Review92:533-44.
6.
———. 2002. Why Americans Split Their Tickets: Campaigns, Competition, and Divided Government. Ann Arbor: University of Michigan Press.
7.
Calvo, Ernesto and Marcelo Escolar .2003. ``The Local Voter: A Geographically Weighted Approach to Ecological Inference.'' American Journal of Political Science47:189-204. Cho, Wendy K. Tam.1998. ``If the Assumption Fits...: A Comment on the King Ecological Inference Solution.'' Political Analysis7:143-63.
8.
Cho, Wendy K. Tam and Brian J. Gaines .2004. ``The Limits of Ecological Inference: The Case of Split-Ticket Voting.'' American Journal of Political Science48(1):152-71.
9.
Cho, Wendy K. Tam and Albert H. Yoon.2001. ``Strange Bedfellows: Politics, Courts, and Statistics: Statistical Expert Testimony in Voting Rights Cases.'' Cornell Journal of Law andPublic Policy102:237-64.
10.
Freedman, David A., Stephen P. Klein, Jerome Sacks, Charles A. Smyth, and Charles G. Everett .1991. ``Ecological Regression and Voting Rights.'' Evaluation Review15: 673-816.
11.
Gay, Claudine.2001. ``The Effect of Black Congressional Representation on Political Participation.'' American Political Science Review953:589-602.
12.
Gimpel, James G. and Jason E. Schuknecht .2004. Patchwork Nation: Sectionalism and Political Change in American Politics. Ann Arbor: University of Michigan Press.
13.
Grofman, Bernard and Michael Migalski .1988. ``Estimating the Extent of Racially Polarized Voting in Multicandidate Elections.'' Sociological Methods & Research164:427-54.
14.
Herron, Michael C. and Kenneth W. Shotts .2004. ``Logical Inconsistency in King's EI-Based Second-Stage Regressions.'' American Journal of Political Science48:172-83.
15.
Imai, Kosuke and Ying Lu.2004. ``Parametric and Non Parametric Bayesian Models for Ecological Inference in 2 x 2 Tables.'' Paper presented at the 2004 Joint Statistical Meeting, the Second Cape Code Monte Carlo Workshop.
16.
Johnston, Ron and Charles Pattie.2000. ``Ecological Inference and Entropy-Maximizing: An Alternative Estimation Procedure for Split-Ticket Voting.'' PoliticalAnalysis84:333-45.
17.
King, Gary.1997. A Solution to the Ecological Inference Problem: Reconstruction Individual Behavior from Aggregate Data. Princeton, NJ : University of Princeton Press.
18.
Kuklinski, James H., Michael D. Cobb, and Martin Gilens.1997. ``Racial Attitudes and the `New South .''' Journal of Politics59:323-49.
19.
Liu, Baodong.2001a. ``The Positive Effect of Black Density on White Crossover Voting: Reconsidering Social Interaction Theory.'' Social Science Quarterly82:602-15.
20.
———. 2001b. ``Racial Context and White Interests: Beyond Black Threat and Racial Tolerance.'' Political Behavior23:157-80.
21.
Perry, Huey L.2003. ``The Evolution and Impact of Biracial Coalition and Black Mayors in Birmingham and New Orleans.'' Pp. 227-54 in Racial Politics in American Cities, edited by R. P. Browning , D. R. Marshall, and D. H. Tabb.New York: Longman.
22.
Richmond, J. (1976). Aggregation and identification. International Economic Review, 17, 47-56.
23.
Robinson, William S.1950. ``Ecological Correlation and the Behavior of Individuals .'' American Sociological Review15:351-7.
24.
Shaw, Daron R.1997. ``Estimating Racially Polarized Voting: A View from the States.'' Political Research Quarterly50:49-74.
25.
Tolbert, Caroline J. and Rodney E. Hero.2001. ``Dealing with Diversity: Racial/Ethnic Context and Social Policy Change.'' Political Research Quarterly54:571-604.
26.
Tomz, Michael and Robert P. Van Houweling .2003. ``How Does Voting Equipment Affect the Racial Gap in Voided Ballot?'' American Journal of Political Science47:46-60.
27.
Voss, D. Stephen.2004. ``Using Ecological Inference for Contextual Research.'' Pp. 69-96 in Ecological Inference: New Methodological Strategies, edited by G. King, O. Rosen, and M.A. Tanner.New York: Cambridge University Press.
28.
Voss, D. Stephen and David Lublin.2001. ``Black Candidates, White Districts: An Appraisal of the 1996 Congressional Elections.'' American Politics Quarterly29:141-82.
29.
Wakefield, J. (2004). A critique of statistical aspects of ecological studies in spatial epidemiology. Environmental and Ecological Statistics, 11, 31-54.
30.
Zax, Jeffrey S.2002. ``Comment on `Estimating the Extent of Racially Polarized Voting in Multicandidate Contests' by Bernard Grofman and Michael Migalski .'' Sociological Methods & Research311:73-84.
31.
———. 2005. ``The Statistical Properties and Empirical Performance of Double Regression.'' Political Analysis131:57-76.
