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

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  • Alan L. Gross

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.

Suggested Citation

  • Alan L. Gross, 1997. "Interval Estimation of Bivariate Correlations With Missing Data on Both Variables: A Bayesian Approach," Journal of Educational and Behavioral Statistics, , vol. 22(4), pages 407-424, December.
    • Handle: RePEc:sae:jedbes:v:22:y:1997:i:4:p:407-424
    DOI: 10.3102/10769986022004407
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