All for One or One for All? A Comparative Study of Grouped Data in Mixed-Effects Additive Bayesian Networks

Additive Bayesian networks (ABNs) provide a flexible framework for modeling complex multivariate dependencies among variables of different distributions, including Gaussian, Poisson, binomial, and multinomial. This versatility makes ABNs particularly attractive in clinical research, where heterogeneous data are frequently collected across distinct groups. However, standard applications either pool all data together, ignoring group-specific variability, or estimate separate models for each group, which may suffer from limited sample sizes. In this work, we extend ABNs to a mixed-effect framework that accounts for group structure through partial pooling, and we evaluate its performance in a large-scale simulation study. We compare three strategies—partial pooling, complete pooling, and no pooling—cross a wide range of network sizes, sparsity levels, group configurations, and sample sizes. Performance is assessed in terms of structural accuracy, parameter estimation accuracy, and predictive performance. Our results demonstrate that partial pooling consistently yields superior structural and parametric accuracy while maintaining robust predictive performance across all evaluated settings for grouped data structures. These findings highlight the potential of mixed-effect ABNs as a versatile approach for learning probabilistic graphical models from grouped data with diverse distributions in real-world applications.