Ecological Inference

Ecological inference is the process of inferring individual level behavior from group-level data or, more specifically, inferring the unobserved cell values in a set of cross-tabulations from the observed marginal totals.

Methods

• The first ecological inference method to combine, in a single model, unit-level deterministic bounds with cross-unit statistical information, unifying two literatures that had been in conflict since 1953. King, Gary, A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data, Princeton: University Press, 1997. (Article: HTML | Replication Data: ICPSR s1132).
• An extension of the work in the above book to use MCMC technology, making models for larger tables possible. King, Gary; Ori Rosen; and Martin Tanner, Binomial-Beta Hierarchical Models for Ecological Inference, Sociological Methods and Research, Vol. 28, No. 1 (August, 1999): 61-90. (Article: PDF | Abstract: HTML)
• This article uses MCMC technology, and a quicker approximation, to make ecological inferences using deterministic and statistical information in larger tables. Rosen, Ori and Wenxin Jiang, Gary King, and Martin A. Tanner, Bayesian and Frequentist Inference for Ecological Inference: The RxC Case, Statistica Neerlandica, Vol. 55, No. 2 (2001): Pp. 134-156. (Article: PDF | Abstract: HTML)
• Outlines some of the history of ecological inference research, and introduces this new book. King, Gary; Ori Rosen; and Martin Tanner, Information in Ecological Inference: An Introduction in King, Rosen, and Tanner, eds., Ecological Inference: New Methodological Strategies, New York: Cambridge University Press, 2004. (Article: PDF)
• Summarizes the explosion of research in ecological inference that has occurred in the previous eight years, all following the key insight of models that include both deterministic and statistical information. King, Gary; Ori Rosen; and Martin A. Tanner, eds., Ecological Inference: New Methodological Strategies, New York: Cambridge University Press, 2004. (Abstract: HTML, Book: PDF)
• Details of an application conducted for the New York Times, including extensions of ecological inference to Bayesian model averaging. Imai, Kosuke and Gary King, Did Illegally Counted Overseas Absentee Ballots Decide the 2000 U.S. Presidential Election?, Perspectives on Politics, Vol. 2, No. 3 (September, 2004): Pp. 537-549. (Article: PDF | Abstract: HTML)
• Related research on aggregation, revealing the logical inconsistency of some popularly used models. Alt, James E.; Gary King; and Curtis Signorino, Aggregation Among Binary, Count, and Duration Models: Estimating the Same Quantities from Different Levels of Data, Political Analysis, Vol. 9, No. 1 (Winter, 2001): Pp. 21-44. (Article: PDF | Abstract: HTML)

Software

• King, Gary. EI: A Program for Ecological Inference, Versions 1996-2003. (Software: EI) Published as part of the Gauss Package by Aptech Systems, Kent, Washington, and as a stand-alone program called EzI: A(n Easy) Program for Ecological Inference, by Kenneth Benoit and me. (Software: EzI)
• The above is published as Gary King. EI: A Program for Ecological Inference, Journal of Statistical Software, (September, 2004): Vol. 11, Issue 7. (Software: EI) Abstract published in Journal of Computational and Graphical Statistics, forthcoming.
• Zelig: Everyone's Statistical Software, includes several methods of ecological inference, and will soon include EI. (Website: Zelig)

Data

• King, Gary and Bradley Palmquist, The Record of American Democracy, 1984-1990, Sociological Methods and Research, Vol. 26, No. 3 (February, 1998): 424-427; and PS: Political Science and Politics, Vol. XXX, No. 4 (December, 1997): 746-747; and ICPSR Bulletin, Vol. XVIII, No. 4 (May, 1998): 1-3. (Website: ROAD)

Discussions and Extensions

• Adolph, Christopher and Gary King, with Michael C. Herron and Kenneth W. Shotts. A Consensus on Second Stage Analyses in Ecological Inference Models, Political Analysis, Vol. 11, No. 1 (Winter, 2003): Pp. 86-94. (Article: PDF | Abstract HTML )
• Adolph, Christopher and Gary King. Analyzing Second Stage Ecological Regressions, Political Analysis, Vol. 11, (Winter, 2003): Pp. 65-76. (Article: PDF)
• King, Gary. Finding New Information for Ecological Inference Models: A Comment on Jon Wakefield, 'Ecological Inference in 2x2 Tables', Journal of the Royal Statistical Society, Series A, Vol. 167 (2004): P. 437. (Article: PDF)
• King, Gary. Isolating Spatial Autocorrelation, Aggregation Bias, and Distributional Violations in Ecological Inference, Political Analysis, Vol. 10, No. 3, (Summer, 2002): 298-300. (Article: PDF)
• King, Gary. Geography, Statistics, and Ecological Inference, Annals of the Association of American Geographers, Vol. 90, No. 3 (September, 2000): Pp. 601-606. (Article: PDF | Abstract: HTML)
• King, Gary, The Future of Ecological Inference Research: A Reply to Freedman et al, Journal of the American Statistical Association, March, 1999. (Article: PDF | Abstract: HTML)