Copula Graphical Models for Heterogeneous Mixed Data

Abstract

This article proposes a graphical model that handles mixed-type, multi-group data. The motivation for such a model originates from real-world observational data, which often contain groups of samples obtained under heterogeneous conditions in space and time, potentially resulting in differences in network structure among groups. Therefore, the iid assumption is unrealistic, and fitting a single graphical model on all data results in a network that does not accurately represent the between group differences. In addition, real-world observational data is typically of mixed discrete-and-continuous type, violating the Gaussian assumption that is typical of graphical models, which leads to the model being unable to adequately recover the underlying graph structure. Both these problems are solved by fitting a different graph for each group, applying the fused group penalty to fuse similar graphs together and by treating the observed data as transformed latent Gaussian data, respectively. The proposed model outperforms related models on learning partial correlations in a simulation study. Finally, the proposed model is applied on real on-farm maize yield data, showcasing the added value of the proposed method in generating new production-ecological hypotheses. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=heteromixgm. Supplementary materials for this article are available online.