New adjusted missing value imputation in multiple regression with simple random sampling and rank set sampling methods

Abstract

This research compared the efficiency of several adjusted missing value imputation methods in multiple regression analysis. The four imputation methods were the following: regression-ratio quartile1,3 (R-RQ1,3) imputation of Al-Omari, Jemain and Ibrahim; adjusted regression-chain ratio quartile1,3 (AR-CRQ1,3) imputation of Kadilar and Cinji; adjusted regression-multivariate ratio quatile1,3 (AR-MRQ1,3) imputation of Feng, Ni, and Zou; and adjusted regression-multivariate chain ratio quartile1,3 (AR-MCRQ1,3) imputation of Lu for each simple random sampling (SRS) and rank set sampling (RSS). The performance measures mean square error (MSE) and mean absolute percentage error (MAPE). The study showed that the AR-MRQ1 method with SRS provided the minimum mean square error for small error variance. However, the AR-MCRQ3 provided the minimum mean square error for a large error variance. Considering all error variance in mean absolute percentage error, the AR-MCRQ1 provided the minimum mean absolute percentage error. The AR-MRQ1 method with RSS provided the minimum mean square error for a small error variance. However, the AR-MCRQ3 provided the minimum mean square error for medium and large error variance. Regarding the mean absolute percentage error measure, the AR-MRQ1 provided the minimum mean absolute percentage error for a small error variance. However, the AR-MCRQ1 provided the minimum mean absolute percentage error for medium and large error variance. For both SRS and RSS, AR-MCRQ1 was the best method for missing value imputation in multiple regression analysis, followed by AR-MCRQ3. Moreover, the RSS estimators provided smaller MSE and MAPE than the SRS estimators. Therefore, the RSS estimators were more efficient than the SRS estimators.