Missing Value Analysis of Numerical Data using Fractional Hot Deck Imputation

Abstract

One of the solutions of missing value in a survey is imputation. Imputation is a method to replace the missing value with the imputed value from a particular technique, such as mean value, median value, etc. This paper specifically discusses a technique that fuses fractional imputation technique and hot-deck imputation technique. Fractional imputation is popular because this imputation tends to produce lower standard error compared to other methods. Unfortunately, fractional imputation tends to extend the number of observations. Because of the observation extension, sampling becomes a solution to produce less observation. Sampling limits the numbers of imputed values (donor) in the observations by using hot deck imputation nature. The imputation that fuses fractional imputation and hot-deck imputation is known as the fractional hot deck. This paper presents three things about fractional hot deck imputation, first, it shows that the result of fractional hot deck imputation produces fewer donor than fractional imputation, but still has a similar property to fractional imputation that presented in linear regression; Second, it presents an additional information about it's effect on modifying it's k-value in discretization step and the standard error of regression; Third, it presents the comparison of standard errors with fractional imputation, listwise deletion, mean imputation, and median imputation.