Bayesian Interval Estimation of Multiple Correlations with Missing Data: A Gibbs Sampling Approach

A Bayesian method for obtaining an interval estimate of the population squared multiple correlation from an incomplete multivariate normal data set is described. The method is applicable to data sets where values are missing on any combination of the dependent and independent variables. Further, the missing data need not be missing in a completely random fashion. The estimates are constructed using a Markov Chain Monte Carlo procedure known as Gibbs Sampling. The important issues of the convergence properties of the Gibbs sampler, the effect of the choice of a reference prior, and the empirical coverage probabilities of the estimates are considered in detail. Investigations using simulated data suggest that the proposed method can yield accurate interval estimates of the population squared multiple correlation.