The R package bgms provides tools for Bayesian analysis of the ordinal Markov random field, a graphical model describing a network of binary and/or ordinal variables (Marsman, van den Bergh, & Haslbeck, in press). A pseudolikelihood is used to approximate the likelihood of the graphical model, and Markov chain Monte Carlo methods are used to simulate from the corresponding pseudoposterior distribution of the graphical model parameters.
The bgm function can be used for a one-sample design and the bgmCompare function can be used for a two-independent-samples design (cf., Marsman, Waldorp, Sekulovski, & Haslbeck, 2024). Both functions can model the selection of effects. In one-sample designs, the bgm function models the presence or absence of edges between pairs of variables in the network. The estimated posterior inclusion probability indicates how plausible it is that a network with an edge between the two corresponding variables produced the observed data, and can be converted into a Bayes factor test for conditional independence.
In two-independent-samples designs, the bgmCompare function models the selection of group differences in edge weights and possibly category thresholds. The estimated posterior inclusion probability indicates how plausible it is that graphical models with a difference in the corresponding edge weight or category threshold generated the data at hand, and can be converted to a Bayes factor test for parameter equivalence.
Why use Markov Random Fields?
Multivariate analysis using graphical models has received much attention in the recent psychological and psychometric literature (Robinaugh et al., 2020; Marsman, & Rhemtulla, 2022; Contreras et al., 2019). Most of these graphical models are Markov Random Field (MRF) models, whose graph structure reflects the partial associations between variables (Kindermann, & Snell 1980). In these models, a missing edge between two variables in the network implies that these variables are independent, given the remaining variables (Lauritzen, 2004). In other words, the remaining variables of the network fully account for the potential association between the unconnected variables.
Why use a Bayesian approach to analyze the MRF?
Testing the structure of the MRF in a one-sample design requires us to determine the plausibility of the opposing hypotheses of conditional dependence and conditional independence. That is, how plausible is it that the observed data come from a network with a structure that includes the edge between two variables compared to a network structure that excludes that edge? Similarly, testing for group differences in the MRF in a two-independent-samples design requires us to determine the plausibility of the opposing hypotheses of parameter difference and parameter equivalence. That is, how plausible is it that the observed data come from two MRFs with a difference in the corresponding edge weight or threshold parameter compared to two MRFs that do not differ in this parameter?
Frequentist approaches are limited in this respect because they can only reject, not support, null hypotheses of conditional independence or parameter equivalence. This leads to the problem that if an edge is excluded, we do not know whether this is because the edge is absent in the population or because we do not have enough data to reject the null hypothesis of independence. Similarly, if a difference is excluded, we do not know whether this is because there is no difference in the parameter between the two groups or because we do not have enough data to reject the null hypothesis of parameter equivalence.
To avoid this problem, we will advocate a Bayesian approach using Bayes factors. In one-sample designs, the inclusion Bayes factor (Huth et al., 2023; Sekulovski et al., 2024) allows us to quantify how much the data support both conditional dependence -evidence of edge presence - or conditional independence -evidence of edge absence. It also allows us to conclude that there is limited support for either hypothesis - an absence of evidence. In two-sample designs, they can be used to quantify how much the data support the hypotheses of parameter difference and equivalence. The output of the bgm and bgmCompare functions can be used to estimate these inclusion Bayes factors.
Installation
The current developmental version can be installed with
if (!requireNamespace("remotes")) {
install.packages("remotes")
}
remotes::install_github("MaartenMarsman/bgms")