Working Paper 34 UNITED NATIONS ECONOMIC COMMISSION FOR EUROPE CONFERENCE OF EUROPEAN STATISTICIANS

1. Missing data problems are ubiquitous in many fields, including official statistics, where one of the common treatments of missing data is ratio imputation (de Waal et al., 2011; Thompson & Washington, 2012; Office for National Statistics, 2014). On the other hand, multiple imputation has been the recommended practice from statisticians (Rubin, 1987; Little & Rubin, 2002). Among statisticians, multiple imputation is known to be the gold standard of treating missing data (Baraldi & Enders, 2010; Cheema, 2014). While ratio imputation is often employed to deal with missing values in practice, the literature is devoid of multiple ratio imputation, leading to a gap between theory and practice. This paper proposes a novel application of the Expectation-Maximization with Bootstrapping (EMB) algorithm to ratio imputation, where multiply-imputed values will be created for each missing value. The objective of this paper is to present the mechanism of multiple ratio imputation and to assess the performance compared to traditional imputation methods. For this purpose, Monte Carlo simulation is applied to the newlydeveloped R-function for multiple ratio imputation. A small application to the 2012 Japanese Economic Census data is also presented to illustrate the usefulness of multiple ratio imputation. Also, this research implemented multiple ratio imputation by the Expectation-Maximization with Bootstrapping (EMB) algorithm in the R statistical environment (to be released soon).