A regression paradox for linear models: Sufficient conditions and relation to Simpson's paradox

American Statistician

Volumn 63, Issue 3, 2009, Pages 218-225

  Chen, Aiyou ^a   Bengtsson, Thomas ^a   Ho, Tin Kam ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

Group effect; Monotone regression; Regression paradox; Reverse regression; Simpson's paradox

Indexed keywords

EID: 77950681306     PISSN: 00031305     EISSN: None     Source Type: Journal    
DOI: 10.1198/tast.2009.08220     Document Type: Article

References (16)

1. Arah, O. (2008), "The Role of Causal Reasoning in Understanding Simpson's Paradox, Lord's Paradox, and the Suppression Effect: Covariate Selection in the Analysis of Observational Data," Emerging Themes in Epidemiology, 5 (5).
2. Bickel, P., Hammel, E., and O'Connell, J. (1975), "Sex Bias in Graduate Admissions: Data From Berkeley," Science, 187, 398-404.
3. Cleveland, W. (1979), "Robust Locally Weighted Regression and Smoothing Scatterplots," Journal of the American Statistical Association, 74, 829-836.
4. Conway, D., and Roberts, H. (1983), "Reverse Regression, Fairness, and Employment Discrimination," Journal of Business & Economic Statistics, 1 (1), 75-85.
5. Conway, D., and Roberts, H. (1984), Rejoinder to Comments on "Reverse Regression, Fairness, and Employment Discrimination," Journal of Business & Economic Statistics, 2 (2), 126-139.
6. Geng, Z. (2006), "Several Untestable Assumptions in Epidemiological Observational Studies, Control Models and Mechanism of Missing Data," Chinese Journal of Disease Control and Prevention, 10 (1), 1-4.
7. Goldberger, A. (1984), "Reverse Regression and Salary Discrimination," The Journal of Human Resources, 19 (3), 293-318.
8. Green, C., and Ferber, M. (1984), "Employment Discrimination: An Empirical Test of Forward versus Reverse Regression," The Journal of Human Resources, 19 (4), 557-569.
9. Holland, P. (1986), "Statistics and Causal Inference" (with discussion), Journal of American Statistical Association, 81, 945-970.
10. Holland, P. W., and Rubin, D. B. (1983), "On Lords Paradox," in Principals of Modern Psychological Measurement, eds. H. Wainer and S. Messnick, Hillsdak, NJ: Lawrence Erlbaum, pp. 3-35.
11. Lord, F. (1967), "A Paradox in the Interpretation of Group Comparisons," Psychological Bulletin, 68, 304-305.
12. Racine, J., and Rilstone, P. (1995), "The Reverse Regression Problem: Statistical Paradox or Artifact of Misspecification?" The Canadian Journal of Economics, 28 (3), 502-531. (Pubitemid 26433046)
13. Samsa, G. (1992), "Resolution of a Regression Paradox in Pretest-Posttest Designs," Journal of Educational Measurement, 29 (4), 321-328.
14. Simpson, E. (1951), "The Interpretation of Interaction in Contingency Tables," Journal of Royal Statistical Society, Ser. B, 13, 238-241.
15. Wainer, H., and Brown, L. (2004), "Two Statistical Paradoxes in the Interpretation of Group Differences: Illustrated With Medical School Admission and Licensing Data," The American Statistician, 58 (2), 117-123. (Pubitemid 38614303)
16. Whiteside, M., and Narayanan, A. (1989), "Reverse Regression, Collinearity, and Employment Discrimination," Journal of Business & Economic Statistics, 7 (3), 403-406.