Movatterモバイル変換

Type:	Package
Title:	Bayesian Analysis of Networks of Binary and/or Ordinal Variables
Version:	0.1.6.1
Date:	2025-10-03
Maintainer:	Maarten Marsman <m.marsman@uva.nl>
Description:	Bayesian variable selection methods for analyzing the structure of a Markov random field model for a network of binary and/or ordinal variables.
Copyright:	Includes datasets 'ADHD' and 'Boredom', which are licensedunder CC-BY 4. See individual data documentation for licenseand citation.
License:	GPL-2 |GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://Bayesian-Graphical-Modelling-Lab.github.io/bgms/
BugReports:	https://github.com/Bayesian-Graphical-Modelling-Lab/bgms/issues
Imports:	Rcpp (≥ 1.0.7), RcppParallel, Rdpack, methods, coda,lifecycle
RdMacros:	Rdpack
LinkingTo:	Rcpp, RcppArmadillo, RcppParallel, dqrng, BH
RoxygenNote:	7.3.3
Depends:	R (≥ 3.5)
LazyData:	true
Encoding:	UTF-8
Suggests:	ggplot2, knitr, parallel, qgraph, rmarkdown, testthat (≥3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
Config/Needs/website:	tidyverse/tidytemplate
NeedsCompilation:	yes
Packaged:	2025-10-03 12:54:27 UTC; maartenmarsman
Author:	Maarten Marsman [aut, cre], Giuseppe Arena [ctb], Karoline Huth [ctb], Nikola Sekulovski [ctb], Don van den Bergh [ctb]
Repository:	CRAN
Date/Publication:	2025-10-04 09:20:02 UTC

bgms: Bayesian Analysis of Networks of Binary and/or Ordinal Variables

Description

TheR packagebgms provides tools for Bayesian analysis ofthe ordinal Markov random field (MRF), a graphical model describing networksof binary and/or ordinal variables (Marsman et al. 2025).The likelihood is approximated via a pseudolikelihood, and Markov chain MonteCarlo (MCMC) methods are used to sample from the corresponding pseudoposteriordistribution of model parameters.

The main entry points are:

• bgm: estimation in a one-sample design.

• bgmCompare: estimation and group comparison in anindependent-sample design.

Both functions support Bayesian effect selection with spike-and-slab priors.

• In one-sample designs,bgm models the presence or absence ofedges between variables. Posterior inclusion probabilities quantify theplausibility of each edge and can be converted into Bayes factors forconditional independence tests.

• bgm can also model communities (clusters) of variables. Theposterior distribution of the number of clusters provides evidence for oragainst clustering (Sekulovski et al. 2025).

• In independent-sample designs,bgmCompare estimates groupdifferences in edge weights and category thresholds. Posterior inclusionprobabilities quantify the evidence for differences and can be convertedinto Bayes factors for parameter equivalence tests(Marsman et al. 2024).

Tools

The package also provides:

1. Simulation of response data from MRFs with a Gibbs sampler(mrfSampler).

2. Posterior estimation and edge selection in one-sample designs(bgm).

3. Posterior estimation and group-difference selection inindependent-sample designs (bgmCompare).

Vignettes

For tutorials and worked examples, see:

• vignette("intro", package = "bgms") — Getting started.

• vignette("comparison", package = "bgms") — Model comparison.

• vignette("diagnostics", package = "bgms") — Diagnostics andspike-and-slab summaries.

Author(s)

Maintainer: Maarten Marsmanm.marsman@uva.nl (ORCID)

Other contributors:

• Giuseppe Arena (ORCID) [contributor]

• Karoline Huth (ORCID) [contributor]

• Nikola Sekulovski (ORCID) [contributor]

• Don van den Bergh (ORCID) [contributor]

References

Marsman M, Waldorp LJ, Sekulovski N, Haslbeck JMB (2024).“Bayes factor tests for group differences in ordinal and binary graphical models.”Retrieved from https://osf.io/preprints/osf/f4pk9.OSF preprint.

Marsman M, van den Bergh D, Haslbeck JMB (2025).“Bayesian analysis of the ordinal Markov random field.”Psychometrika,90, 146–-182.

Sekulovski N, Arena G, Haslbeck JMB, Huth KBS, Friel N, Marsman M (2025).“A Stochastic Block Prior for Clustering in Graphical Models.”Retrieved fromhttps://osf.io/preprints/psyarxiv/29p3m_v1.OSF preprint.

See Also

Useful links:

• https://Bayesian-Graphical-Modelling-Lab.github.io/bgms/

• Report bugs athttps://github.com/Bayesian-Graphical-Modelling-Lab/bgms/issues

ADHD Symptom Checklist for Children Aged 6–8 Years

Description

This dataset includes ADHD symptom ratings for 355 children aged 6 to 8 years from theChildren’s Attention Project (CAP) cohort (Silk et al. 2019). The sampleconsists of 146 children diagnosed with ADHD and 209 without a diagnosis. Symptoms wereassessed through structured interviews with parents using the NIMH Diagnostic InterviewSchedule for Children IV (DISC-IV) (Shaffer et al. 2000). The checklistincludes 18 items: 9 Inattentive (I) and 9 Hyperactive/Impulsive (HI). Each item is binary(1 = present, 0 = absent).

Usage

data("ADHD")

Format

A matrix with 355 rows and 19 columns.

group

ADHD diagnosis: 1 = diagnosed, 0 = not diagnosed

avoid

Often avoids, dislikes, or is reluctant to engage in tasksthat require sustained mental effort (I)

closeatt

Often fails to give close attention to details or makescareless mistakes in schoolwork, work, or other activities (I)

distract

Is often easily distracted by extraneous stimuli (I)

forget

Is often forgetful in daily activities (I)

instruct

Often does not follow through on instructions and fails tofinish schoolwork, chores, or duties in the workplace (I)

listen

Often does not seem to listen when spoken to directly(I)

loses

Often loses things necessary for tasks or activities (I)

org

Often has difficulty organizing tasks and activities (I)

susatt

Often has difficulty sustaining attention in tasks or playactivities (I)

blurts

Often blurts out answers before questions have been completed(HI)

fidget

Often fidgets with hands or feet or squirms in seat(HI)

interrupt

Often interrupts or intrudes on others (HI)

motor

Is often "on the go" or often acts as if "driven by a motor"(HI)

quiet

Often has difficulty playing or engaging in leisure activitiesquietly (HI)

runs

Often runs about or climbs excessively in situations in whichit is inappropriate (HI)

seat

Often leaves seat in classroom or in other situations in whichremaining seated is expected (HI)

talks

Often talks excessively (HI)

turn

Often has difficulty awaiting turn (HI)

Source

Silk et al. (2019).Data retrieved fromdoi:10.1371/journal.pone.0211053.s004.Licensed under the CC-BY 4.0: https://creativecommons.org/licenses/by/4.0/

References

Shaffer D, Fisher P, Lucas CP, Dulcan MK, Schwab-Stone ME (2000).“NIMH Diagnostic Interview Schedule for Children Version IV (NIMH DISC-IV): description, differences from previous versions, and reliability of some common diagnoses.”Journal of the American Academy of Child & Adolescent Psychiatry,39, 28–38.doi:10.1097/00004583-200001000-00014, PMID: 10638065.

Silk TJ, Malpas CB, Beare R, Efron D, Anderson V, Hazell P, Jongeling B, Nicholson JM, Sciberras E (2019).“A network analysis approach to ADHD symptoms: More than the sum of its parts.”PLOS ONE,14(1), e0211053.doi:10.1371/journal.pone.0211053.

Short Boredom Proneness Scale Responses

Description

This dataset includes responses to the 8-item Short Boredom Proneness Scale (SBPS),a self-report measure of an individual's susceptibility to boredom(Martarelli et al. 2023). Items were rated on a 7-point Likert scaleranging from 1 ("strongly disagree") to 7 ("strongly agree"). The scale was administeredin either English (Struk et al. 2015) or French (translated by (Martarelli et al. 2023)).

Usage

data("Boredom")

Format

A matrix with 986 rows and 9 columns. Each row corresponds to a respondent.

language

Language in which the SBPS was administered: "en" = English, "fr" = French

loose_ends

I often find myself at “loose ends,” not knowing what todo.

entertain

I find it hard to entertain myself.

repetitive

Many things I have to do are repetitive and monotonous.

stimulation

It takes more stimulation to get me going than mostpeople.

motivated

I don't feel motivated by most things that I do.

keep_interest

In most situations, it is hard for me to findsomething to do or see to keep me interested.

sit_around

Much of the time, I just sit around doing nothing.

half_dead_dull

Unless I am doing something exciting, even dangerous,I feel half-dead and dull.

Source

Martarelli et al. (2023).Data retrieved fromhttps://osf.io/qhux8.Licensed under the CC-BY 4.0: https://creativecommons.org/licenses/by/4.0/

References

Martarelli CS, Baillifard A, Audrin C (2023).“A Trait-Based Network Perspective on the Validation of the French Short Boredom Proneness Scale.”European Journal of Psychological Assessment,39(6), 390–399.doi:10.1027/1015-5759/a000718.

Struk AA, Carriere JSA, Cheyne JA, Danckert J (2015).“A Short Boredom Proneness Scale: Development and Psychometric Properties.”Assessment,24(3), 346–359.doi:10.1177/1073191115609996.

PTSD Symptoms in Wenchuan Earthquake Survivors Who Lost a Child

Description

This dataset contains responses to 17 items assessing symptoms of post-traumatic stress disorder (PTSD)in Chinese adults who survived the 2008 Wenchuan earthquake and lost at least one child in the disaster(McNally et al. 2015). Participants completed the civilian version of the Posttraumatic Checklist,with each item corresponding to a DSM-IV PTSD symptom. Items were rated on a 5-point Likert scale from"not at all" to "extremely," indicating the degree to which the symptom bothered the respondent in thepast month.

Usage

data("Wenchuan")

Format

A matrix with 362 rows and 17 columns. Each row represents a participant.

intrusion

Repeated, disturbing memories, thoughts, or images of astressful experience from the past?

dreams

Repeated, disturbing dreams of a stressful experience fromthe past?

flash

Suddenly acting or feeling as if a stressful experience werehappening again (as if you were reliving it)?

upset

Feeling very upset when something reminded you of a stressfulexperience from the past?

physior

Having physical reactions (e.g., heart pounding, troublebreathing, sweating) when something reminded you of a stressful experiencefrom the past?

avoidth

Avoiding thinking about or talking about a stressfulexperience from the past or avoiding having feelings related to it?

avoidact

Avoiding activities or situations because they reminded youof a stressful experience from the past?

amnesia

Trouble remembering important parts of a stressfulexperience from the past?

lossint

Loss of interest in activities that you used to enjoy?

distant

Feeling distant or cut off from other people?

numb

Feeling emotionally numb or being unable to have lovingfeelings for those close to you?

future

Feeling as if your future will somehow be cut short?

sleep

Trouble falling or staying asleep?

anger

Feeling irritable or having angry outbursts?

concen

Having difficulty concentrating?

hyper

Being "super-alert" or watchful or on guard?

startle

Feeling jumpy or easily startled?

Source

https://psychosystems.org/wp-content/uploads/2014/10/Wenchuan.csv

References

McNally RJ, Robinaugh DJ, Wu GWY, Wang L, Deserno MK, Borsboom D (2015).“Mental disorders as causal systems: A network approach to posttraumatic stress disorder.”Clinical Psychological Science,6, 836–849.doi:10.1177/2167702614553230.

Bayesian Estimation or Edge Selection for Markov Random Fields

Description

Thebgm function estimates the pseudoposterior distribution ofcategory thresholds (main effects) and pairwise interaction parameters of aMarkov Random Field (MRF) model for binary and/or ordinal variables.Optionally, it performs Bayesian edge selection using spike-and-slabpriors to infer the network structure.

Usage

bgm(  x,  variable_type = "ordinal",  baseline_category,  iter = 1000,  warmup = 1000,  pairwise_scale = 2.5,  main_alpha = 0.5,  main_beta = 0.5,  edge_selection = TRUE,  edge_prior = c("Bernoulli", "Beta-Bernoulli", "Stochastic-Block"),  inclusion_probability = 0.5,  beta_bernoulli_alpha = 1,  beta_bernoulli_beta = 1,  dirichlet_alpha = 1,  lambda = 1,  na_action = c("listwise", "impute"),  update_method = c("nuts", "adaptive-metropolis", "hamiltonian-mc"),  target_accept,  hmc_num_leapfrogs = 100,  nuts_max_depth = 10,  learn_mass_matrix = FALSE,  chains = 4,  cores = parallel::detectCores(),  display_progress = c("per-chain", "total", "none"),  seed = NULL,  interaction_scale,  burnin,  save,  threshold_alpha,  threshold_beta)

Arguments

Details

This function models the joint distribution of binary and ordinal variablesusing a Markov Random Field, with support for edge selection through Bayesianvariable selection. The statistical foundation of the model is described inMarsman et al. (2025), where the ordinalMRF model and its Bayesian estimation procedure were first introduced. Whilethe implementation inbgms has since been extended and updated (e.g.,alternative priors, parallel chains, HMC/NUTS warmup), it builds on thatoriginal framework.

Key components of the model are described in the sections below.

Value

A list of class"bgms" with posterior summaries, posterior meanmatrices, and access to raw MCMC draws. The object can be passed toprint(),summary(), andcoef().

Main components include:

• posterior_summary_main: Data frame with posterior summaries(mean, sd, MCSE, ESS, Rhat) for category threshold parameters.

• posterior_summary_pairwise: Data frame with posteriorsummaries for pairwise interaction parameters.

• posterior_summary_indicator: Data frame with posteriorsummaries for edge inclusion indicators (ifedge_selection = TRUE).

• posterior_mean_main: Matrix of posterior mean thresholds(rows = variables, cols = categories or parameters).

• posterior_mean_pairwise: Symmetric matrix of posterior meanpairwise interaction strengths.

• posterior_mean_indicator: Symmetric matrix of posterior meaninclusion probabilities (if edge selection was enabled).

• Additional summaries returned whenedge_prior = "Stochastic-Block". For more details about this priorsee Sekulovski et al. (2025).

  • posterior_summary_pairwise_allocations: Data frame withposterior summaries (mean, sd, MCSE, ESS, Rhat) for the pairwisecluster co-occurrence of the nodes. This serves to indicatewhether the estimated posterior allocations,co-clustering matrixand posterior cluster probabilities (see blow) have converged.

  • posterior_coclustering_matrix: a symmetric matrix ofpairwise proportions of occurrence of every variable. This matrixcan be plotted to visually inspect the estimated number of clustersand visually inspect nodes that tend to switch clusters.

  • posterior_mean_allocations: A vector with the posterior meanof the cluster allocations of the nodes. This is calculated using the methodproposed in Dahl (2009).

  • posterior_mode_allocations: A vector with the posteriormode of the cluster allocations of the nodes.

  • posterior_num_blocks: A data frame with the estimatedposterior inclusion probabilities for all the possible number of clusters.

• raw_samples: A list of raw MCMC draws per chain:

  main

  List of main effect samples.

  pairwise

  List of pairwise effect samples.

  indicator

  List of indicator samples(if edge selection enabled).

  allocations

  List of cluster allocations(if SBM prior used).

  nchains

  Number of chains.

  niter

  Number of post–warmup iterations per chain.

  parameter_names

  Named lists of parameter labels.

• arguments: A list of function call arguments and metadata(e.g., number of variables, warmup, sampler settings, package version).

Thesummary() method prints formatted posterior summaries, andcoef() extracts posterior mean matrices.

NUTS diagnostics (tree depth, divergences, energy, E-BFMI) are includedinfit$nuts_diag ifupdate_method = "nuts".

Ordinal Variables

The function supports two types of ordinal variables:

Regular ordinal variables:Assigns a category threshold parameter to each response category except thelowest. The model imposes no additional constraints on the distribution ofcategory responses.

Blume-Capel ordinal variables:Assume a baseline category (e.g., a “neutral” response) and score responsesby distance from this baseline. Category thresholds are modeled as:

\mu_{c} = \alpha \cdot c + \beta \cdot (c - b)^2

where:

• \mu_{c}: category threshold for categoryc

• \alpha: linear trend across categories

• \beta: preference toward or away from the baseline

  • If\beta < 0, the model favors responses near the baselinecategory;

  • if\beta > 0, it favors responses farther away (i.e.,extremes).

• b: baseline category

Edge Selection

Whenedge_selection = TRUE, the function performs Bayesian variableselection on the pairwise interactions (edges) in the MRF usingspike-and-slab priors.

Supported priors for edge inclusion:

• Bernoulli: Fixed inclusion probability across edges.

• Beta-Bernoulli: Inclusion probability is assigned a Betaprior distribution.

• Stochastic-Block: Cluster-based edge priors with Beta,Dirichlet, and Poisson hyperpriors.

All priors operate via binary indicator variables controlling the inclusionor exclusion of each edge in the MRF.

Prior Distributions

• Pairwise effects: Modeled with a Cauchy (slab) prior.

• Main effects: Modeled using a beta-primedistribution.

• Edge indicators: Use either a Bernoulli, Beta-Bernoulli, orStochastic-Block prior (as above).

Sampling Algorithms and Warmup

Parameters are updated within a Gibbs framework, but the conditionalupdates can be carried out using different algorithms:

• Adaptive Metropolis–Hastings: Componentwise random–walkupdates for main effects and pairwise effects. Proposal standarddeviations are adapted during burn–in via Robbins–Monro updatestoward a target acceptance rate.

• Hamiltonian Monte Carlo (HMC): Joint updates of allparameters using fixed–length leapfrog trajectories. Step size istuned during warmup via dual–averaging; the diagonal mass matrix canalso be adapted iflearn_mass_matrix = TRUE.

• No–U–Turn Sampler (NUTS): An adaptive extension of HMCthat dynamically chooses trajectory lengths. Warmup uses a stagedadaptation schedule (fast–slow–fast) to stabilize step size and, ifenabled, the mass matrix.

Whenedge_selection = TRUE, updates of edge–inclusion indicatorsare carried out with Metropolis–Hastings steps. These are switched onafter the core warmup phase, ensuring that graph updates occur only oncethe samplers’ tuning parameters (step size, mass matrix, proposal SDs)have stabilized.

After warmup, adaptation is disabled. Step size and mass matrix arefixed at their learned values, and proposal SDs remain constant.

Warmup and Adaptation

The warmup procedure inbgm is based on the multi–stage adaptationschedule used in Stan (Stan Development Team 2023). Warmup iterations aresplit into several phases:

• Stage 1 (fast adaptation): A short initial intervalwhere only step size (for HMC/NUTS) is adapted, allowing the chainto move quickly toward the typical set.

• Stage 2 (slow windows): A sequence of expanding,memoryless windows where both step size and, iflearn_mass_matrix = TRUE, the diagonal mass matrix areadapted. Each window ends with a reset of the dual–averaging schemefor improved stability.

• Stage 3a (final fast interval): A short interval at theend of the core warmup where the step size is adapted one final time.

• Stage 3b (proposal–SD tuning): Only active whenedge_selection = TRUE under HMC/NUTS. In this phase,Robbins–Monro adaptation of proposal standard deviations isperformed for the Metropolis steps used in edge–selection moves.

• Stage 3c (graph selection warmup): Also only relevantwhenedge_selection = TRUE. At the start of this phase, arandom graph structure is initialized, and Metropolis–Hastingsupdates for edge inclusion indicators are switched on.

Whenedge_selection = FALSE, the total number of warmup iterationsequals the user–specifiedburnin. Whenedge_selection = TRUEandupdate_method is"nuts" or"hamiltonian-mc",the schedule automatically appends additional Stage-3b and Stage-3cintervals, so the total warmup is strictly greater than the requestedburnin.

After all warmup phases, the sampler transitions to the sampling phasewith adaptation disabled. Step size and mass matrix (for HMC/NUTS) arefixed at their learned values, and proposal SDs remain constant.

This staged design improves stability of proposals and ensures that bothlocal parameters (step size) and global parameters (mass matrix, proposalSDs) are tuned before collecting posterior samples.

For adaptive Metropolis–Hastings runs, step size and mass matrixadaptation are not relevant. Proposal SDs are tuned continuously duringburn–in using Robbins–Monro updates, without staged fast/slow intervals.

Missing Data

Ifna_action = "listwise", observations with missing values areremoved.Ifna_action = "impute", missing values are imputed during Gibbssampling.

References

Dahl DB (2009).“Modal clustering in a class of product partition models.”Bayesian Analysis,4(2), 243–264.doi:10.1214/09-BA409.

Marsman M, van den Bergh D, Haslbeck JMB (2025).“Bayesian analysis of the ordinal Markov random field.”Psychometrika,90, 146–-182.

Sekulovski N, Arena G, Haslbeck JMB, Huth KBS, Friel N, Marsman M (2025).“A Stochastic Block Prior for Clustering in Graphical Models.”Retrieved fromhttps://osf.io/preprints/psyarxiv/29p3m_v1.OSF preprint.

Stan Development Team (2023).Stan Modeling Language Users Guide and Reference Manual.Version 2.33,https://mc-stan.org/docs/.

See Also

vignette("intro", package = "bgms") for a worked example.

Examples

# Run bgm on subset of the Wenchuan datasetfit = bgm(x = Wenchuan[, 1:5])# Posterior inclusion probabilitiessummary(fit)$indicator# Posterior pairwise effectssummary(fit)$pairwise

Bayesian Estimation and Variable Selection for Group Differences in Markov Random Fields

Description

ThebgmCompare function estimates group differences in categorythreshold parameters (main effects) and pairwise interactions (pairwiseeffects) of a Markov Random Field (MRF) for binary and ordinal variables.Groups can be defined either by supplying two separate datasets (x andy) or by a group membership vector. Optionally, Bayesian variableselection can be applied to identify differences across groups.

Usage

bgmCompare(  x,  y,  group_indicator,  difference_selection = TRUE,  variable_type = "ordinal",  baseline_category,  difference_scale = 1,  difference_prior = c("Bernoulli", "Beta-Bernoulli"),  difference_probability = 0.5,  beta_bernoulli_alpha = 1,  beta_bernoulli_beta = 1,  pairwise_scale = 2.5,  main_alpha = 0.5,  main_beta = 0.5,  iter = 1000,  warmup = 1000,  na_action = c("listwise", "impute"),  update_method = c("nuts", "adaptive-metropolis", "hamiltonian-mc"),  target_accept,  hmc_num_leapfrogs = 100,  nuts_max_depth = 10,  learn_mass_matrix = FALSE,  chains = 4,  cores = parallel::detectCores(),  display_progress = c("per-chain", "total", "none"),  seed = NULL,  main_difference_model,  reference_category,  main_difference_scale,  pairwise_difference_scale,  pairwise_difference_prior,  main_difference_prior,  pairwise_difference_probability,  main_difference_probability,  pairwise_beta_bernoulli_alpha,  pairwise_beta_bernoulli_beta,  main_beta_bernoulli_alpha,  main_beta_bernoulli_beta,  interaction_scale,  threshold_alpha,  threshold_beta,  burnin,  save)

Arguments

Details

This function extends the ordinal MRF frameworkMarsman et al. (2025) to multiplegroups. The basic idea of modeling, analyzing, and testing groupdifferences in MRFs was introduced inMarsman et al. (2024), wheretwo–group comparisons were conducted using adaptive Metropolis sampling.The present implementation generalizes that approach to more than twogroups and supports additional samplers (HMC and NUTS) with staged warmupadaptation.

Key components of the model:

Value

A list of class"bgmCompare" containing posterior summaries,posterior mean matrices, and raw MCMC samples:

• posterior_summary_main_baseline,posterior_summary_pairwise_baseline: summaries of baselinethresholds and pairwise interactions.

• posterior_summary_main_differences,posterior_summary_pairwise_differences: summaries of groupdifferences in thresholds and pairwise interactions.

• posterior_summary_indicator: summaries of inclusionindicators (ifdifference_selection = TRUE).

• posterior_mean_main_baseline,posterior_mean_pairwise_baseline: posterior mean matrices(legacy style).

• raw_samples: list of raw draws per chain for main,pairwise, and indicator parameters.

• arguments: list of function call arguments and metadata.

Thesummary() method prints formatted summaries, andcoef() extracts posterior means.

NUTS diagnostics (tree depth, divergences, energy, E-BFMI) are includedinfit$nuts_diag ifupdate_method = "nuts".

Pairwise Interactions

For variablesi andj, the group-specific interaction isrepresented as:

\theta_{ij}^{(g)} = \phi_{ij} + \delta_{ij}^{(g)},

where\phi_{ij} is the baseline effect and\delta_{ij}^{(g)} are group differences constrained to sum to zero.

Ordinal Variables

Regular ordinal variables: category thresholds are decomposed into abaseline plus group differences for each category.

Blume–Capel variables: category thresholds are quadratic in thecategory index, with both the linear and quadratic terms split into abaseline plus group differences.

Variable Selection

Whendifference_selection = TRUE, spike-and-slab priors areapplied to difference parameters:

• Bernoulli: fixed prior inclusion probability.

• Beta–Bernoulli: inclusion probability given a Beta prior.

Sampling Algorithms and Warmup

Parameters are updated within a Gibbs framework, using the samesampling algorithms and staged warmup scheme described inbgm:

• Adaptive Metropolis–Hastings: componentwise random–walkproposals with Robbins–Monro adaptation of proposal SDs.

• Hamiltonian Monte Carlo (HMC): joint updates with fixedleapfrog trajectories; step size and optionally the mass matrix areadapted during warmup.

• No–U–Turn Sampler (NUTS): an adaptive HMC variant withdynamic trajectory lengths; warmup uses the same staged adaptationschedule as HMC.

For details on the staged adaptation schedule (fast–slow–fast phases),seebgm. In addition, whendifference_selection = TRUE, updates of inclusion indicators aredelayed until late warmup. In HMC/NUTS, this appends two extra phases(Stage-3b and Stage-3c), so that the total number of warmup iterationsexceeds the user-specifiedwarmup.

After warmup, adaptation is disabled: step size and mass matrix are fixedat their learned values, and proposal SDs remain constant.

References

Marsman M, Waldorp LJ, Sekulovski N, Haslbeck JMB (2024).“Bayes factor tests for group differences in ordinal and binary graphical models.”Retrieved from https://osf.io/preprints/osf/f4pk9.OSF preprint.

Marsman M, van den Bergh D, Haslbeck JMB (2025).“Bayesian analysis of the ordinal Markov random field.”Psychometrika,90, 146–-182.

See Also

vignette("comparison", package = "bgms") for a worked example.

Examples

## Not run: # Run bgmCompare on subset of the Boredom datasetx = Boredom[Boredom$language == "fr", 2:6]y = Boredom[Boredom$language != "fr", 2:6]fit <- bgmCompare(x, y)# Posterior inclusion probabilitiessummary(fit)$indicator# Bayesian model averaged main effects for the groupscoef(fit)$main_effects_groups# Bayesian model averaged pairwise effects for the groupscoef(fit)$pairwise_effects_groups## End(Not run)

Extract Coefficients from a bgmCompare Object

Description

Returns posterior means for raw parameters (baseline + differences)and group-specific effects from abgmCompare fit, as well as inclusion indicators.

Usage

## S3 method for class 'bgmCompare'coef(object, ...)

Arguments

Value

A list with components:

main_effects_raw

Posterior means of the raw main-effect parameters(variables x [baseline + differences]).

pairwise_effects_raw

Posterior means of the raw pairwise-effect parameters(pairs x [baseline + differences]).

main_effects_groups

Posterior means of group-specific main effects(variables x groups), computed as baseline plus projected differences.

pairwise_effects_groups

Posterior means of group-specific pairwise effects(pairs x groups), computed as baseline plus projected differences.

indicators

Posterior mean inclusion probabilities as a symmetric matrix,with diagonals corresponding to main effects and off-diagonals to pairwise effects.

Extract Coefficients from a bgms Object

Description

Returns the posterior mean thresholds, pairwise effects, and edge inclusion indicators from abgms model fit.

Usage

## S3 method for class 'bgms'coef(object, ...)

Arguments

Value

A list with the following components:

main

Posterior mean of the category threshold parameters.

pairwise

Posterior mean of the pairwise interaction matrix.

indicator

Posterior mean of the edge inclusion indicators (if available).

Extractor Functions for bgms Objects

Description

Extractor Functions for bgms Objects

Usage

extract_arguments(bgms_object)## S3 method for class 'bgms'extract_arguments(bgms_object)## S3 method for class 'bgmCompare'extract_arguments(bgms_object)extract_indicators(bgms_object)## S3 method for class 'bgms'extract_indicators(bgms_object)## S3 method for class 'bgmCompare'extract_indicators(bgms_object)extract_posterior_inclusion_probabilities(bgms_object)## S3 method for class 'bgms'extract_posterior_inclusion_probabilities(bgms_object)extract_sbm(bgms_object)## S3 method for class 'bgms'extract_sbm(bgms_object)## S3 method for class 'bgmCompare'extract_posterior_inclusion_probabilities(bgms_object)extract_indicator_priors(bgms_object)## S3 method for class 'bgms'extract_indicator_priors(bgms_object)## S3 method for class 'bgmCompare'extract_indicator_priors(bgms_object)extract_pairwise_interactions(bgms_object)## S3 method for class 'bgms'extract_pairwise_interactions(bgms_object)## S3 method for class 'bgmCompare'extract_pairwise_interactions(bgms_object)extract_category_thresholds(bgms_object)## S3 method for class 'bgms'extract_category_thresholds(bgms_object)## S3 method for class 'bgmCompare'extract_category_thresholds(bgms_object)extract_group_params(bgms_object)## S3 method for class 'bgmCompare'extract_group_params(bgms_object)extract_edge_indicators(bgms_object)extract_pairwise_thresholds(bgms_object)

Details

These functions extract various components from objects returned by the 'bgm()' function,such as edge indicators, posterior inclusion probabilities, and parameter summaries.

Internally, indicator samples were stored in '$gamma' (pre-0.1.4) and'$indicator' (0.1.4–0.1.5). As of **bgms 0.1.6.0**, they are stored in'$raw_samples$indicators'. Access via older names is supported but deprecated.

Posterior inclusion probabilities are computed from edge indicators.

Internally, indicator samples were stored in '$gamma' (pre-0.1.4) and'$indicator' (0.1.4–0.1.5). As of **bgms 0.1.6.0**, they are stored in'$raw_samples$indicator'. Access via older names is supported but deprecated.

Category thresholds were previously stored in '$main_effects' (pre-0.1.4) and'$posterior_mean_main' (0.1.4–0.1.5). As of **bgms 0.1.6.0**, they are storedin '$posterior_summary_main'. Access via older names is supported but deprecated.

Functions

- 'extract_arguments()' – Extract model arguments- 'extract_indicators()' – Get sampled edge indicators- 'extract_posterior_inclusion_probabilities()' – Posterior edge inclusion probabilities- 'extract_pairwise_interactions()' – Posterior mean of pairwise interactions- 'extract_category_thresholds()' – Posterior mean of category thresholds- 'extract_indicator_priors()' – Prior structure used for edge indicators- 'extract_sbm' – Extract stochastic block model parameters (if applicable)

Sample observations from the ordinal MRF

Description

This function samples states from the ordinal MRF using a Gibbs sampler. TheGibbs sampler is initiated with random values from the response options,after which it proceeds by simulating states for each variable from a logisticmodel using the other variable states as predictor variables.

Usage

mrfSampler(  no_states,  no_variables,  no_categories,  interactions,  thresholds,  variable_type = "ordinal",  reference_category,  iter = 1000)

Arguments

Details

There are two modeling options for the category thresholds. The defaultoption assumes that the category thresholds are free, except that the firstthreshold is set to zero for identification. The user then only needs tospecify the thresholds for the remaining response categories. This option isuseful for any type of ordinal variable and gives the user the most freedomin specifying their model.

The Blume-Capel option is specifically designed for ordinal variables thathave a special type of reference_category category, such as the neutralcategory in a Likert scale. The Blume-Capel model specifies the followingquadratic model for the threshold parameters:

\mu_{\text{c}} = \alpha \times \text{c} + \beta \times (\text{c} - \text{r})^2,

where\mu_{\text{c}} is the threshold for category c(which now includes zero),\alpha offers a linear trendacross categories (increasing threshold values if\alpha > 0 and decreasing threshold values if\alpha <0), if\beta < 0, it offers anincreasing penalty for responding in a category further away from thereference_category category r, while\beta > 0 suggests apreference for responding in the reference_category category.

Value

Ano_states byno_variables matrix of simulated states ofthe ordinal MRF.

Examples

# Generate responses from a network of five binary and ordinal variables.no_variables = 5no_categories = sample(1:5, size = no_variables, replace = TRUE)Interactions = matrix(0, nrow = no_variables, ncol = no_variables)Interactions[2, 1] = Interactions[4, 1] = Interactions[3, 2] =  Interactions[5, 2] = Interactions[5, 4] = .25Interactions = Interactions + t(Interactions)Thresholds = matrix(0, nrow = no_variables, ncol = max(no_categories))x = mrfSampler(no_states = 1e3,               no_variables = no_variables,               no_categories = no_categories,               interactions = Interactions,               thresholds = Thresholds)# Generate responses from a network of 2 ordinal and 3 Blume-Capel variables.no_variables = 5no_categories = 4Interactions = matrix(0, nrow = no_variables, ncol = no_variables)Interactions[2, 1] = Interactions[4, 1] = Interactions[3, 2] =  Interactions[5, 2] = Interactions[5, 4] = .25Interactions = Interactions + t(Interactions)Thresholds = matrix(NA, no_variables, no_categories)Thresholds[, 1] = -1Thresholds[, 2] = -1Thresholds[3, ] = sort(-abs(rnorm(4)), decreasing = TRUE)Thresholds[5, ] = sort(-abs(rnorm(4)), decreasing = TRUE)x = mrfSampler(no_states = 1e3,               no_variables = no_variables,               no_categories = no_categories,               interactions = Interactions,               thresholds = Thresholds,               variable_type = c("b","b","o","b","o"),               reference_category = 2)

Print method for 'bgmCompare' objects

Description

Minimal console output for 'bgmCompare' fit objects.

Usage

## S3 method for class 'bgmCompare'print(x, ...)

Arguments

Print method for 'bgms' objects

Description

Minimal console output for 'bgms' fit objects.

Usage

## S3 method for class 'bgms'print(x, ...)

Arguments

Summary method for 'bgmCompare' objects

Description

Returns posterior summaries and diagnostics for a fitted 'bgmCompare' model.

Usage

## S3 method for class 'bgmCompare'summary(object, ...)

Arguments

Value

An object of class 'summary.bgmCompare' with posterior summaries.

Summary method for 'bgms' objects

Description

Returns posterior summaries and diagnostics for a fitted 'bgms' model.

Usage

## S3 method for class 'bgms'summary(object, ...)

Arguments

Value

An object of class 'summary.bgms' with posterior summaries.