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Models, assumptions and model checking in ecological regressions

Author

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  • Andrew Gelman
  • David K. Park
  • Stephen Ansolabehere
  • Phillip N. Price
  • Lorraine C. Minnite

Abstract

Ecological regression is based on assumptions that are untestable from aggregate data. However, these assumptions seem more questionable in some applications than in others. There has been some research on implicit models of individual data underlying aggregate ecological regression modelling. We discuss ways in which these implicit models can be checked from aggregate data. We also explore the differences in applications of ecological regressions in two examples: estimating the effect of radon on lung cancer in the United States and estimating voting patterns for different ethnic groups in New York City.

Suggested Citation

  • Andrew Gelman & David K. Park & Stephen Ansolabehere & Phillip N. Price & Lorraine C. Minnite, 2001. "Models, assumptions and model checking in ecological regressions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 101-118.
    • Handle: RePEc:bla:jorssa:v:164:y:2001:i:1:p:101-118
    DOI: 10.1111/1467-985X.00190
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    Cited by:

    1. Aiyar, Anaka & Cummins, Joseph R., 2021. "An age profile perspective on two puzzles in global child health: The Indian Enigma & economic growth," Journal of Development Economics, Elsevier, vol. 148(C).
    2. Herrera Gómez, Marcos, 2008. "Una introducción al análisis multinivel: ¿La demanda individual de salud es afectada por el médico de cabecera? [An introduction to multilevel analysis: Is the individual demand for health is affec," MPRA Paper 35267, University Library of Munich, Germany.
    3. Puig, Xavier & Ginebra, Josep, 2014. "A cluster analysis of vote transitions," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 328-344.
    4. Samira Rousselière & Gaëlle Petit & Thomas Coisnon & Anne Musson & Damien Rousselière, 2022. "A few drinks behind—Alcohol price and income elasticities in Europe: A microeconometric note," Journal of Agricultural Economics, Wiley Blackwell, vol. 73(1), pages 301-315, February.
    5. 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.
    6. Roberto Colombi & Antonio Forcina, 2016. "Latent class models for ecological inference on voters transitions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 501-517, November.
    7. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    8. Staniswalis, Joan G., 2006. "On fitting generalized non-linear models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1818-1839, April.
    9. Amanda Kennard, 2021. "My Brother’s Keeper: Other-regarding preferences and concern for global climate change," The Review of International Organizations, Springer, vol. 16(2), pages 345-376, April.
    10. Bernard Grofman & Matt A. Barreto, 2009. "A Reply to Zax's (2002) Critique of Grofman and Migalski (1988)," Sociological Methods & Research, , vol. 37(4), pages 599-617, May.
    11. Gillian A. Lancaster & Mick Green & Steven Lane, 2006. "Reducing bias in ecological studies: an evaluation of different methodologies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 681-700, October.
    12. D. James Greiner & Kevin M. Quinn, 2009. "R×C ecological inference: bounds, correlations, flexibility and transparency of assumptions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 67-81, January.
    13. 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.
    14. Marta Benet & Patricia Celi-Medina & Montserrat Fernández & Sandra Ezquerra, 2022. "The COVID-19 Pandemic in Care Homes: An Exploration of Its Impact across Regions in Spain," IJERPH, MDPI, vol. 19(15), pages 1-16, August.

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