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

City University of New York

The posterior distribution of the bivariate correlation (_xy) is analytically derived given a data set consisting N₁ cases measured on both x and y, N₂ cases measured only on x, and N₃ cases measured only ony. The posterior distribution is shown to be a function of the subsample sizes, the sample correlation (r_xy) computed from the N₁ 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 _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 _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.

Key Words: Bayesian statistics • correlations • missing data

Journal of Educational and Behavioral Statistics, Vol. 22, No. 4, 407-424 (1997)
DOI: 10.3102/10769986022004407


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