Imputation Methods Based on Cluster-Wise Linear Regression: A Mathematical Programming Approach

Abstract

In some applications, datasets may form several homogeneous clusters with respect to the relationship between the explanatory variables and the response variable. The presence of missing values in such datasets requires the use of two or more regression models subjected to a single objective function, which best summarizes the structure of the dataset, for imputing the missing values. This can be done using the cluster-wise linear regression model. The cluster-wise linear regression model is estimated through a mathematical programming approach based on the available data. Three imputation methods based on cluster-wise linear regression are used in this article. They are the largest cluster, the simple weighting, and the inverse distance weighting imputation methods. The cluster-wise linear regression is then integrated in the proposed imputation methods, to fill in the missing values in the response variable. The simulation study shows a decent performance for the proposed imputation methods based on cluster-wise linear regression.