Interval Estimation of Bivariate Correlations With Missing Data on Both Variables: A Bayesian Approach

Alan L. Gross

Journal of Educational and Behavioral Statistics, 1997, vol. 22, issue 4, 407-424

Abstract: The posterior distribution of the bivariate correlation ( Ï xy ) is analytically derived given a data set consisting N 1 cases measured on both x and y, N 2 cases measured only on x , and N 3 cases measured only on y . The posterior distribution is shown to be a function of the subsample sizes, the sample correlation ( r xy ) computed from the N 1 complete cases, a set of four statistics which measure the extent to which the missing data are not missing completely at random, and the specified prior distribution for Ï xy . A sampling study suggests that in small ( N = 20 ) and moderate ( N = 50 ) sized samples, posterior Bayesian interval estimates will dominate maximum likelihood based estimates in terms of coverage probability and expected interval widths when the prior distribution for Ï xy is simply uniform on (0, 1). The advantage of the Bayesian method when more informative priors based on beta densities are employed is not as consistent.

Keywords: Bayesian statistics; correlations; missing data (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:22:y:1997:i:4:p:407-424

DOI: 10.3102/10769986022004407

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