A0482
Title: Bayesian edge selection in mixed Markov random fields for ordinal and continuous variables
Authors: Maarten Marsman - University of Amsterdam (Netherlands) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Abstract: Markov random field (MRF) graphical models are widely used in network psychometrics to model the network structure of psychometric variables. While existing methods typically handle either continuous or ordinal data, many psychological datasets include both. A novel MRF model is introduced for mixed ordinal and continuous variables. The model generalizes the ordinal MRF proposed by a recent study and is a special case of the conditional Gaussian graphical model. To estimate the network structure, a Bayesian variable selection approach is proposed using spike-and-slab priors on the edge weights. This prior structure aligns with existing methods for discrete MRFs and enables hierarchical modeling of the network structure. However, two challenges arise. First, the edge weight matrix must lie within the space of positive definite matrices, resulting in a joint prior with an intractable normalizing constant. This is addressed using a Metropolis algorithm that samples directly from the constrained space. Second, the MRF likelihood itself is computationally intractable. To overcome this, approximation strategies are explored, including pseudolikelihood methods. It is planned to implement the methodology in the bgms R package and integrate it into the JASP software platform for applied researchers.
