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Copula graphical models for heterogeneous mixed data

Sjoerd HermesJoost van HeerwaardenPariya Behrouzi
Oct 2022
摘要
This article proposes a graphical model that can handle mixed-type,multi-group data. The motivation for such a model originates from real-worldobservational data, which often contain groups of samples obtained underheterogeneous conditions in space and time, potentially resulting indifferences in network structure among groups. Therefore, the i.i.d. assumptionis unrealistic, and fitting a single graphical model on all data results in anetwork that does not accurately represent the between group differences. Inaddition, real-world observational data is typically of mixed-type, violatingthe Gaussian assumption that is typical of graphical models, which leads to themodel being unable to adequately recover the underlying graph structure. Theproposed model takes into account these properties of data, by treatingobserved data as transformed latent Gaussian data, and thereby allowing for theattractive properties of the Gaussian distribution such as partial correlationsfrom the inverse covariance matrix to be utilised. In an extensive simulationstudy, the proposed model is evaluated against alternative models, where theproposed model is better able to recover the true underlying graph structurefor different groups. Finally, the proposed model is applied on realproduction-ecological data pertaining to on-farm maize yield in order toshowcase the added value of the proposed method in generating new hypothesesfor production ecologists.
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