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Simple methods for ecological inference in 2×2 tables

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  • R. L. Chambers
  • D. G. Steel

Abstract

This paper considers inference about the individual level relationship between two dichotomous variables based on aggregated data. It is known that such analyses suffer from ‘ecological bias’, caused by the lack of homogeneity of this relationship across the groups over which the aggregation occurs. Two new methods for overcoming this bias, one based on local smoothing and the other a simple semiparametric approach, are developed and evaluated. The local smoothing approach performs best when it is used with a covariate which accounts for some of the variation in the relationships across groups. The semiparametric approach performed well in our evaluation even without such auxiliary information

Suggested Citation

  • R. L. Chambers & D. G. Steel, 2001. "Simple methods for ecological inference in 2×2 tables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 175-192.
    • Handle: RePEc:bla:jorssa:v:164:y:2001:i:1:p:175-192
    DOI: 10.1111/1467-985X.00195
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    Cited by:

    1. Pelzer, B. & Eisinga, R. & Franses, Ph.H.B.F., 2001. "Inferring transition probabilities from repeated cross sections: a cross-level inference approach to US presidential voting," Econometric Institute Research Papers EI 2001-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Irene L. Hudson & Linda Moore & Eric J. Beh & David G. Steel, 2010. "Ecological inference techniques: an empirical evaluation using data describing gender and voter turnout at New Zealand elections, 1893–1919," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(1), pages 185-213, January.
    3. Beh, Eric J., 2010. "The aggregate association index," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1570-1580, June.
    4. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables (with discussion)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-445, July.
    5. Antonio Forcina & Davide Pellegrino, 2019. "Estimation of voter transitions and the ecological fallacy," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1859-1874, July.

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