Objective Bayesian Edge Screening and Structure Selection for Ising Networks

Abstract

The Ising model is one of the most widely analyzed graphical models in network psychometrics. Unfortunately, popular approaches to parameter estimation and structure selection for the Ising model cannot naturally express uncertainty about the estimated parameters or selected structures. To address this issue, this paper offers an objective Bayesian approach to parameter estimation and structure selection for the Ising model. Our approach builds on George and McCulloch's continuous spike-and-slab approach (1993, Journal of the American Statistical Association, 88, 881--889). We show that our methods consistently select the correct structure and provide a new objective method to set the spike-and-slab hyperparameters. To circumvent the exploration of the complete structure space, which is too large in practical situations, we propose a novel approach that first screens for promising edges and then only explore the space instantiated by these edges. We apply our proposed methods to estimate the network of depression and alcohol use disorder symptoms from symptom scores of over 26,000 subjects.

Modeling Alcohol Use Disorder as a Set of Interconnected Symptoms - Assessing Differences between Clinical and Population Samples and Across External Factors

“…The width of this interval can be adapted through a precision parameter. Marsman et al (2020) proposed using a precision of .997 (i.e., corresponding to a 99,7 % credible interval), as this value closely matched the performance of eLasso in simulations. Here, we found the results of .975 precision to be in line with eLasso for an Ising model (van Borkulo et al, 2015).…”

“…To address our first question, we estimated an Ising model (i.e., a binary network model) separately for each subgroup and compared strength of connection as well as the underlying topological structures. To estimate each model, we used a recently developed Bayesian approach implementing a shrinkage prior to reduce weak links in the network to zero (Marsman et al, 2020). A major advantage of this Bayesian approach over the classical lasso approach is the ability to express the uncertainty in the estimated structure.…”

“…We followed the procedure detailed in Marsman et al (2020), using its respective R-package rbinnet which is based on a Gibbs-variable selection approach (George & McCulloch, 1993). A continuous spike and slab mixture of zero-centered normal was stipulated on the interactions in the network.…”

The Theoretical and Statistical Ising Model: A Practical Guide in R

“…We first perform Bayesian estimation with rbinnet, which is followed by a robustness analysis of the result [82]. We use rbinnet to compute two hypotheses per edge, H 0 : ω ij = 0 and H 1 : ω ij = 0.…”

“…Bayesian Estimation with rbinnet a . rbinnet is a new package for the Bayesian estimation of Ising models [82]. First, it uses pseudo-likelihood estimation to find good candidate values for each edge through the fit_pseduolikelihood() function.…”