Sample Correlation Coefficients Based on Survey Data Under Regression Imputation

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Abstract
Regression imputation is commonly used to compensate for item nonresponse when auxiliary data are available. It is common practice to compute survey estimators by treating imputed values as observed data and using the standard unbiased (or nearly unbiased) estimation formulas designed for the case of no nonresponse. Although the commonly used regression imputation method preserves unbiasedness for population marginal totals (i.e., survey estimators computed from imputed data are still nearly unbiased), it does not preserve unbiasedness for population correlation coefficients. A joint regression imputation method is proposed that preserves unbiasedness for marginal totals, second moments, and correlation coefficients. Some simulation results show that the joint regression imputation method produces not only sample correlation coefficients that are nearly unbiased, but also estimates that are more stable than those produced by marginal nonrandom regression imputation when correlation coefficients are in a certain range. Variance estimation for sample correlation coefficients under joint regression imputation is also studied, using a jackknife method that takes imputation into account.