Combining Aggregate and Individual Level Data to Estimate an Individual Level Correlation Coefficient

Archived Abstract of Former PSC Researcher

Raghunathan, Trivellore, P.K. Diehr, and A.D. Cheadle. 2003. "Combining Aggregate and Individual Level Data to Estimate an Individual Level Correlation Coefficient." Journal of Educational and Behavioral Statistics, 28(1): 1-19.

Methods are developed that use aggregate data, possibly based on a large number of individuals, and individual level data, from a small fraction of individuals from the same or similar population, to eliminate ecological bias inherent in the analysis of aggregate data. The primary focus is on estimating the individual level correlation coefficient but the proposed methodology can be extended to estimate regression coefficients. Two approaches, the method of moments and the maximum likelihood, are developed for a bivariate distribution, but can be extended to a multivariate distribution. The method of moments develops a corrected estimate of the within-group covariance matrix, which is then used to estimate the individual level correlation and regression coefficients. The second method assumes bivariate normality and maximizes the combined likelihood function based on the two data sets. The maximum likelihood estimates are obtained using the EM-algorithm. A simulation study investigates the repeated sampling properties of these procedures in terms of bias and the mean square error of the point estimates and the actual coverage of the confidence intervals. The maximum likelihood estimates are almost unbiased and the confidence intervals are well calibrated for simulation conditions considered. The method of moments estimates have the same desirable properties for some simulation conditions. Under all conditions, the correlation coefficient between aggregate variables is severely biased as an estimate of the individual level correlation coefficient.

Ecological Fallacy/ Em-Algorithm/ Maximum Likelihood/ Method of Moments/ Random Effects/ Ecological Fallacy

Browse | Search | Next

PSC In The News

RSS Feed icon

Shaefer comments on the Cares Act impact in negating hardship during COVID-19 pandemic

Heller comments on lasting safety benefit of youth employment programs

More News


Dean Yang's Combatting COVID-19 in Mozambique study releases Round 1 summary report

Help Establish Standard Data Collection Protocols for COVID-19 Research

More Highlights

Connect with PSC follow PSC on Twitter Like PSC on Facebook