Imputation of missing data using Gaussian linear cluster-weighted modeling

The theory of missing data addresses statistical methods for handling cases where some values for the variable of interest are absent. However, much of statistical theory traditionally assumes fully observed data. One approach to manage incomplete data sets is imputation, where missing values are estimated based on certain criteria. In this work, we present a novel imputation methodology for univariate missing data patterns, leveraging fully observed auxiliary variables. The model assumes the nonobserved variable is continuous and that auxiliary variables provide valuable information to enhance imputation accuracy. Within a fully Bayesian framework, our method employs a flexible mixture of multivariate normal distributions to jointly model the response and auxiliary variables. Using the properties of Gaussian cluster-weighted modeling, we develop a predictive model to impute the missing values based on the auxiliary data. We illustrate the performance of our method through simulation studies and real-world data, demonstrating its imputation capacity across various scenarios and comparing it to existing methods in the literature.