300 – Innovations in and Applications of Imputation
An Algorithm of Generalized Robust Ratio Model Estimation for Imputation
Seiji Takata
Ministry of Internal Affairs and Communication
Hiroe Tsubaki
The Institute of Statistical Mathematics
Kazumi Wada
National Statistics Center
This paper proposes an algorithm of simultaneous robust estimation for the generalized ratio model proposed by Wada and Sakashita (2017) with an implemented R function. It helps to abbreviate the model selection process prior to imputation in the course of survey data processing. Wada and Sakashita (2017) robustify the ratio model by introducing homoscedastic quasi-error term to determine robust weights for each observation based on the idea of M-estimation. They also extended the ratio model so that the errors are proportional to the explanatory variable to a different powers. The algorithm we propose is to estimate the power of the explanatory variable together with the ratio of objective variables robustly. The estimate of power may not be very accurate as with the weighted two-stage least squares; however, the accuracy of ratio matters for imputation, since the value of the power is not used for estimation of the objective variable. Therefore, the proposed algorithm could be of use as long as the estimation of the ratio has good accuracy regardless of the power.