Combining aggregate and individual level data to estimate an individual level correlation coefficient

Journal of Educational and Behavioral Statistics

Volumn 28, Issue 1, 2003, Pages 1-19

  Raghunathan, Trivellore E ^a   Diehr, Paula K ^b   Cheadle, Allen D ^b  

^a UNIVERSITY OF MICHIGAN SCHOOL OF PUBLIC HEALTH   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Ecological fallacy; EM algorithm; Maximum likelihood; Method of moments; Random effects

Indexed keywords

EID: 0037595501     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986028001001     Document Type: Article

References (19)

1. Aptech Systems, Inc. (1992). The GAUSS system version 3.0. [computer program]. Author.
2. Bryk, A. S. (1992). Hierarchical linear models: Applications and data analysis methods, Newbury Park, CA: Sage Publications.
3. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete observations. Journal of Royal Statistical Society, Series B, 39, 1-38.
4. Diehr, P., Koepsell, T., Cheadle, A., Psaty, B. M., Wagner, E., & Curry, S. (1993). Do communities differ in health behaviors? Journal of Clinical Epidemiology, 46, 1141-1149.
5. Firebaugh, G. (1978). A rule for infering individual-level relationships from aggregate data. American Sociological Review, 43, 557-572.
6. Goldstein, H. (1995). Multilevel statistical models, New York: Halsted Press.
7. Greenland, S., & Robins, J. (1994). Invited commentary: Ecologic studies-biases, misconceptions, and counterexamples. American Journal of Epidemiology, 139, 747-760.
8. Hammond, J. L. (1973). Two sources of error in ecological correlations. American Sociological Review, 38, 764-778.
9. Kraemer, H. C. (1978). Individual and ecological correlation in a general context. Behavioral Science, 23, 67-72.
10. Little, R. J. A., & Rubin, D. B. (1987). Statistical analysis with missing data. New York: Wiley.
11. Longford, N. T. (1993). Random coefficient models, Oxford, UK: Oxford University Press.
12. Pearson, K. (1902). On the mathematical theory of errors of judgment, with special reference to the personal equation. Philosophical Transactions of the Royal Society, Series A, 192, 235-299.
13. Piantadosi, S., Byar, D. P., & Green, S. B. (1988). The ecological fallacy. American Journal of Epidemiology, 127, 893-904.
14. Prentice, R. L., & Shepard, L. (1995). Aggregate data studies of disease risk factors. Biometrika, 82, 113-125.
15. Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. American Sociological Review, 15, 351-357.
16. Shepard, L., & Prentice, R. L. (1995). On the reliability and precision of within and between population estimates of relative rate parameters. Biometrics, 51, 731-742.
17. Smith, A. M. F., & Gelfand, A. E. (1991). Sampling based approaches to calculating marginal densities. Journal of American Statistical Association, 85, 398-409.
18. Steel, D. G., & Holt, D. (1996). Analyzing and adjusting aggregation effects: The ecological fallacy revisited. International Statistical Review, 64, 39-60.
19. Yule, G. H. (1903). Notes on the theory of association of attributes in statistics. Biometrika, 2, 121-134.