A Comparative Study of Imputation Methods for Estimation of Missing Values of Per Capita Expenditure in Central Java

Abstract

Missing values in repeated measurements have attracted concerns from researchers in the last few years. For many years, the standard statistical methods for repeated measurements have been developed assuming that the data was complete. The standard statistical methods cannot produce good estimates if the data suffered substantially by missing values. To overcome this problem the imputation methods could be used. This paper discusses three imputation methods namely the Yates method, expectation-maximization (EM) algorithm, and Markov Chain Monte Carlo (MCMC) method. These methods were used to estimate the missing values of per-capita expenditure data at sub-districts level in Central Java. The performance of these imputation methods is evaluated by comparing the mean square error (MSE) and mean absolute error (MAE) of the resulting estimates using linear mixed models. It is showed that MSE and MAE produced by the Yates method are lower than the MSE and MAE resulted from both the EM algorithm and the MCMC method. Therefore, the Yates method is recommended to impute the missing values of per capita expenditure at sub-district level.