Bayesian networks (BNs) are widely used tools for the modeling of complex dependencies among variables. However, their application to multilevel or clustered data remains constrained, especially in scenarios involving multiple random effects, due to a lack of methods and more pressing, efficient computational frameworks. In this article, we propose an innovative framework, INLA-MBN, that integrates multilevel BNs (MBNs) with the integrated nested Laplace approximation (INLA), thereby facilitating efficient structure and parameter learning in both longitudinal and cross-sectional multilevel data contexts. To the best of our knowledge, this is the first implementation of INLA for BNs that involves more than one correlated random effect. More precisely, we advance existing research by modeling longitudinal data with two correlated random effects and multilevel cross-sectional data with more than two correlated random effects. Our approach encompasses both Gaussian and hybrid MBNs that incorporate Gaussian and categorical nodes. Through an exhaustive simulation study, we demonstrate that INLA-MBN exhibit superior performance compared to networks based on maximum likelihood estimation, particularly, in scenarios characterized by small group sizes or limited repeated measurements per subject. INLA-MBN achieves a fully inferred MBN, while negating the cost associated with MBNs based on Markov Chain Monte Carlo. The proposed method was also applied to real-life longitudinal child morbidity data to demonstrate its practical applicability.
B. E. Yirdaw, L. K. Debusho, J. van Niekerk et al.· Statistical Methods in Medic...· 0 citations
Specifying a prior over the space of correlation matrices is a persistent challenge in Bayesian analysis. The space is a curved manifold whose dimension grows quadratically with the number of variables, making substantive prior beliefs difficult to encode.\\ We propose a distance-based prior that assigns mass decaying exponentially in the Fisher arc-length distance from a user-specified reference correlation matrix, enabling shrinkage toward any target correlation structure rather than being confined to the identity matrix. Formally, this is constructed as a Penalised Complexity prior, but its interpretation shifts accordingly: unless the chosen target represents a structurally simpler state, the shrinkage penalises deviation rather than complexity in the usual sense. To accommodate conditional independence constraints, we introduce a parameterisation that constructs the correlation matrix via the Cholesky factor of the inverse correlation matrix with respect to a user-supplied graph, thereby reducing the number of free parameters from one per variable pair to one per graph edge. The prior is proper for every positive value of its rate parameter, accommodates correlations of either sign under any graph structure, and reduces to a fully unstructured prior when the graph is complete. A direct sampling algorithm is provided, enabling prior predictive checks and sensitivity analysis, implemented within the \texttt{graphpcor} package.
A. Freni-Sterrantino, J. V. Niekerk, E. Krainski et al.· 1 citation
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