Goodness (of fit) of Imputation Accuracy: The GoodImpact Analysis

Abstract: In statistical survey analysis, (partial) non-responders are integral elements during data acquisition. Treating missing values during data preparation and data analysis is therefore a non-trivial underpinning. Focusing on different data sets from the Federal Statistical Office of Germany (DESTATIS), we investigate various imputation methods regarding their imputation accuracy. Since the latter is not uniquely determined in theory and practice, we study different measures for assessing imputation accuracy: Beyond the most common measures, the normalized-root mean squared error (NRMSE) and the proportion of false classification (PFC), we put a special focus on (distribution) distance- and association measures for assessing imputation accuracy. The aim is to deliver guidelines for correctly assessing distributional accuracy after imputation. Our empirical findings indicate a discrepancy between the NRMSE resp. PFC and distance measures. While the latter measure distributional similarities, NRMSE and PFC focus on data reproducibility. We realize that a low NRMSE or PFC seem not to imply lower distributional discrepancies. Although several measures for assessing distributional discrepancies exist, our results indicate that not all of them are suitable for evaluating imputation-induced differences.