Imputation of missing data using multivariate Gaussian Linear Cluster-Weighted Modeling

Abstract: Missing data arises when certain values are not recorded or observed for variables of interest. However, most of the statistical theory assume complete data availability. To address incomplete databases, one approach is to fill the gaps corresponding to the missing information based on specific criteria, known as imputation. In this study, we propose a novel imputation methodology for databases with non-response units by leveraging additional information from fully observed auxiliary variables. We assume that the variables included in the database are continuous and that the auxiliary variables, which are fully observed, help to improve the imputation capacity of the model. Within a fully Bayesian framework, our method utilizes a flexible mixture of multivariate normal distributions to jointly model the response and auxiliary variables. By employing the principles of Gaussian Cluster-Weighted modeling, we construct a predictive model to impute the missing values by leveraging information from the covariates. We present simulation studies and a real data illustration to demonstrate the imputation capacity of our method across various scenarios, comparing it to other methods in the literature