Home > Publications . Search All . Browse All . Country . Browse PSC Pubs . PSC Report Series

PSC In The News

RSS Feed icon

Stephenson says homophobia among gay men raises risk of intimate partner violence

Frey says having more immigrants with higher birth rates fills need in the US

Inglehart's work on the rise of populism cited in NYT

More News

Highlights

Savolainen wins Outstanding Contribution Award for study of how employment affects recidivism among past criminal offenders

Giving Blueday at ISR focuses on investing in the next generation of social scientists

Pfeffer and Schoeni cover the economic and social dimensions of wealth inequality in this special issue

PRB Policy Communication Training Program for PhD students in demography, reproductive health, population health

More Highlights

Next Brown Bag

Mon, Jan 23, 2017 at noon:
H. Luke Shaefer

Trivellore Raghunathan photo

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

Publication Abstract

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.

Browse | Search : All Pubs | Next