Type:	Package
Title:	Bayesian Analysis of Networks of Binary and/or Ordinal Variables
Version:	0.1.4.2
Date:	2024-12-03
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. Details of the implemented methods can be found in: Marsman, van den Bergh, and Haslbeck (in press) <doi:10.31234/osf.io/ukwrf>.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://maartenmarsman.github.io/bgms/
BugReports:	https://github.com/MaartenMarsman/bgms/issues
Imports:	Rcpp (≥ 1.0.7), Rdpack, methods
RdMacros:	Rdpack
LinkingTo:	Rcpp, RcppProgress
RoxygenNote:	7.3.2
Depends:	R (≥ 2.10)
LazyData:	true
Encoding:	UTF-8
Suggests:	knitr, qgraph, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
Config/Needs/website:	tidyverse/tidytemplate
NeedsCompilation:	yes
Packaged:	2024-12-05 09:44:17 UTC; maartenmarsman
Author:	Maarten Marsman [aut, cre], Karoline Huth [ctb], Nikola Sekulovski [ctb], Don van den Bergh [ctb]
Repository:	CRAN
Date/Publication:	2024-12-05 10:20:06 UTC

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

Description

The R package bgms provides tools for Bayesian analysis of graphical models describing networks of variables. The package uses Markov chain Monte Carlo methods combined with a pseudolikelihood approach to estimate the posterior distribution of model parameters.

Gibbs variable selection (George and McCulloch 1993) is used to model the underlying network structure of the graphical model. By imposing a discrete spike and slab prior on the pairwise interactions, it is possible to shrink the interactions to exactly zero. The Gibbs sampler embeds a Metropolis approach for mixtures of mutually singular distributions (Gottardo and Raftery 2008) to account for the discontinuity at zero. The goal is to provide these tools for Markov Random Field (MRF) models for a wide range of variable types in the bgms package, and it currently provides them for analyzing networks of binary and/or ordinal variables (Marsman et al. in press).

While the goal is to provide the above tools for Markov Random Field (MRF) models for a wide range of variable types in the bgms package, it currently provides tools for analyzing networks of binary and/or ordinal variables (Marsman et al. in press).

MRFs are a special class of graphical models whose graph structure reflects the conditional associations between their variables, making them useful for testing for conditional independence or dependence. For example, the inclusion Bayes factor tests for conditional independence or dependence of a pair of variables in the network by comparing the predictive adequacy of models that include the edge between these variables and models that exclude the edge. (Huth et al. 2023; Sekulovski et al. in press).

The bgms package offers several tools for analyzing the structure of the MRF:

1. Simulate response data from the MRF using the Gibbs sampler.

   • Simulate mrfSampler.

2. Estimate the posterior distribution of the MRF's parameters and possibly its network structure using Gibbs variable selection.

   • Bayesian estimation or Bayesian edge selection with bgm.

Author(s)

Maintainer: Maarten Marsman m.marsman@uva.nl (ORCID)

Other contributors:

• Karoline Huth (ORCID) [contributor]

• Nikola Sekulovski (ORCID) [contributor]

• Don van den Bergh (ORCID) [contributor]

References

George EI, McCulloch RE (1993). “Variable selection via Gibbs sampling.” Journal of the American Statistical Association, 88, 881–889. doi:10.1080/01621459.1993.10476353.

Gottardo R, Raftery AE (2008). “Markov Chain Monte Carlo With Mixtures of Mutually Singular Distributions.” Journal of Computational and Graphical Statistics, 17, 949–975. doi:10.1198/106186008X386102.

Huth K, de Ron J, Goudriaan AE, Luigjes K, Mohammadi R, van Holst RJ, Wagenmakers E, Marsman M (2023). “Bayesian analysis of cross-sectional networks: A tutorial in R and JASP.” Advances in Methods and Practices in Psychological Science, 6, 1–18doi.

Marsman M, van den Bergh D, Haslbeck JMB (in press). “Bayesian analysis of the ordinal Markov random field.” Psychometrika.

Sekulovski N, Keetelaar S, Huth K, Wagenmakers E, van Bork R, van den Bergh D, Marsman M (in press). “Testing conditional independence in psychometric networks: An analysis of three bayesian methods.” Multivariate Behavioral Research. doi:10.1080/00273171.2024.2345915.

See Also

Useful links:

• https://maartenmarsman.github.io/bgms/

• Report bugs at https://github.com/MaartenMarsman/bgms/issues

Post-traumatic stress disorder symptoms of Wenchuan earthquake survivors

Description

A data set containing items measuring symptoms of posttraumatic stress disorder (PTSD) (McNally et al. 2015). Participants were 362 Chinese adults who survived the Wenchuan earthquake and lost at least one child in the disaster. PTSD symptoms were reported using the civilian version of the Posttraumatic Checklist, which consists of 17 items, each assessing one of the DSM-IV symptoms of PTSD. Participants rated each item on a five-point scale ranging from “not at all” to “extremely” to indicate how much the symptom bothered them in the past month.

Usage

data("Wenchuan")

Format

A matrix with 362 rows and 17 columns:

intrusion

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

dreams

Repeated, disturbing dreams of a stressful experience from the past?

flash

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

upset

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

physior

Having physical reactions (e.g., heart pounding, trouble breathing, sweating) when something reminded you of a stressful experience from the past?

avoidth

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

avoidact

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

amnesia

Trouble remembering important parts of a stressful experience 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 loving feelings 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

http://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 edge selection or Bayesian estimation for a Markov random field model for binary and/or ordinal variables.

Description

The function bgm explores the joint pseudoposterior distribution of parameters and possibly edge indicators for a Markov Random Field model for mixed binary and ordinal variables.

Usage

bgm(
  x,
  variable_type = "ordinal",
  reference_category,
  iter = 10000,
  burnin = 500,
  interaction_scale = 2.5,
  threshold_alpha = 0.5,
  threshold_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,
  na.action = c("listwise", "impute"),
  save = FALSE,
  display_progress = TRUE
)

Arguments

Details

Currently, bgm supports two types of ordinal variables. The regular, default, ordinal variable type has no restrictions on its distribution. Every response category except the first receives its own threshold parameter. The Blume-Capel ordinal variable assumes that there is a specific reference category, such as the “neutral” in a Likert scale, and responses are scored in terms of their distance to this reference category. Specifically, the Blume-Capel model specifies the following quadratic 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. The parameter \alpha models a linear trend across categories, such that \alpha > 0 leads to an increasing number of observations in higher response categories and \alpha <0 leads to a decreasing number of observations in higher response categories. The parameter \beta models the response style in terms of an offset with respect to the reference category r; if \beta<0 there is a preference to respond in the reference category (i.e., the model introduces a penalty for responding in a category further away from the reference_category category r), while if \beta > 0 there is preference to score in the extreme categories further away from the reference_category category.

The Bayesian estimation procedure (edge_selection = FALSE) simply estimates the threshold and pairwise interaction parameters of the ordinal MRF, while the Bayesian edge selection procedure (edge_selection = TRUE) also models the probability that individual edges should be included or excluded from the model. Bayesian edge selection imposes a discrete spike and slab prior distribution on the pairwise interactions. By formulating it as a mixture of mutually singular distributions, the function can use a combination of Metropolis-Hastings and Gibbs sampling to create a Markov chain that has the joint posterior distribution as an invariant. The current option for the slab distribution is a Cauchy with an optional scaling parameter. The slab distribution is also used as the prior for the interaction parameters for Bayesian estimation. A beta-prime distribution is used for the exponent of the category parameters. For Bayesian edge selection, two prior distributions are implemented for the edge inclusion variables (i.e., the prior probability that an edge is included); the Bernoulli prior and the Beta-Bernoulli prior.

Value

If save = FALSE (the default), the result is a list of class “bgms” containing the following matrices with model-averaged quantities:

• indicator: A matrix with p rows and p columns, containing the posterior inclusion probabilities of individual edges.

• interactions: A matrix with p rows and p columns, containing model-averaged posterior means of the pairwise associations.

• thresholds: A matrix with p rows and max(m) columns, containing model-averaged category thresholds. In the case of “blume-capel” variables, the first entry is the parameter for the linear effect and the second entry is the parameter for the quadratic effect, which models the offset to the reference category.

If save = TRUE, the result is a list of class “bgms” containing:

• indicator: A matrix with iter rows and p * (p - 1) / 2 columns, containing the edge inclusion indicators from every iteration of the Gibbs sampler.

• interactions: A matrix with iter rows and p * (p - 1) / 2 columns, containing parameter states from every iteration of the Gibbs sampler for the pairwise associations.

• thresholds: A matrix with iter rows and sum(m) columns, containing parameter states from every iteration of the Gibbs sampler for the category thresholds.

Column averages of these matrices provide the model-averaged posterior means.

In addition to the analysis results, the bgm output lists some of the arguments of its call. This is useful for post-processing the results.

References

Geng J, Bhattacharya A, Pati D (2019). “Probabilistic community detection with unknown number of communities.” Journal of the American Statistical Association, 114, 893–905. doi:10.1080/01621459.2018.1458618.

Examples

 #Store user par() settings
 op <- par(no.readonly = TRUE)

 ##Analyse the Wenchuan dataset

 # Here, we use 1e4 iterations, for an actual analysis please use at least
 # 1e5 iterations.
 fit = bgm(x = Wenchuan)


 #------------------------------------------------------------------------------|
 # INCLUSION - EDGE WEIGHT PLOT
 #------------------------------------------------------------------------------|

 par(mar = c(6, 5, 1, 1))
 plot(x = fit$interactions[lower.tri(fit$interactions)],
      y = fit$indicator[lower.tri(fit$indicator)], ylim = c(0, 1),
      xlab = "", ylab = "", axes = FALSE, pch = 21, bg = "gray", cex = 1.3)
 abline(h = 0, lty = 2, col = "gray")
 abline(h = 1, lty = 2, col = "gray")
 abline(h = .5, lty = 2, col = "gray")
 mtext("Posterior Mode Edge Weight", side = 1, line = 3, cex = 1.7)
 mtext("Posterior Inclusion Probability", side = 2, line = 3, cex = 1.7)
 axis(1)
 axis(2, las = 1)


 #------------------------------------------------------------------------------|
 # EVIDENCE - EDGE WEIGHT PLOT
 #------------------------------------------------------------------------------|

 #For the default choice of the structure prior, the prior odds equal one:
 prior.odds = 1
 posterior.inclusion = fit$indicator[lower.tri(fit$indicator)]
 posterior.odds = posterior.inclusion / (1 - posterior.inclusion)
 log.bayesfactor = log(posterior.odds / prior.odds)
 log.bayesfactor[log.bayesfactor > 5] = 5

 par(mar = c(5, 5, 1, 1) + 0.1)
 plot(fit$interactions[lower.tri(fit$interactions)], log.bayesfactor, pch = 21, bg = "#bfbfbf",
      cex = 1.3, axes = FALSE, xlab = "", ylab = "", ylim = c(-5, 5.5),
      xlim = c(-0.5, 1.5))
 axis(1)
 axis(2, las = 1)
 abline(h = log(1/10), lwd = 2, col = "#bfbfbf")
 abline(h = log(10), lwd = 2, col = "#bfbfbf")

 text(x = 1, y = log(1 / 10), labels = "Evidence for Exclusion", pos = 1,
      cex = 1.7)
 text(x = 1, y = log(10), labels = "Evidence for Inclusion", pos = 3, cex = 1.7)
 text(x = 1, y = 0, labels = "Absence of Evidence", cex = 1.7)
 mtext("Log-Inclusion Bayes Factor", side = 2, line = 3, cex = 1.5, las = 0)
 mtext("Posterior Mean Interactions ", side = 1, line = 3.7, cex = 1.5, las = 0)


 #------------------------------------------------------------------------------|
 # THE MEDIAN PROBABILITY NETWORK
 #------------------------------------------------------------------------------|

 tmp = fit$interactions[lower.tri(fit$interactions)]
 tmp[posterior.inclusion < 0.5] = 0

 median.prob.model = matrix(0, nrow = ncol(Wenchuan), ncol = ncol(Wenchuan))
 median.prob.model[lower.tri(median.prob.model)] = tmp
 median.prob.model = median.prob.model + t(median.prob.model)

 rownames(median.prob.model) = colnames(Wenchuan)
 colnames(median.prob.model) = colnames(Wenchuan)

 library(qgraph)
 qgraph(median.prob.model,
        theme = "TeamFortress",
        maximum = .5,
        fade = FALSE,
        color = c("#f0ae0e"), vsize = 10, repulsion = .9,
        label.cex = 1.1, label.scale = "FALSE",
        labels = colnames(Wenchuan))

 #Restore user par() settings
 par(op)

Bayesian variable selection or Bayesian estimation for differences in the Markov random field model for binary and/or ordinal variables in two independent samples.

Description

The bgmCompare function estimates the pseudoposterior distribution of the parameters of a Markov Random Field model for mixed binary and ordinal variables, and the differences in pairwise interactions and category thresholds between two groups. The groups are assumed to be two independent samples.

Usage

bgmCompare(
  x,
  y,
  difference_selection = TRUE,
  main_difference_model = c("Free", "Collapse", "Constrain"),
  variable_type = "ordinal",
  reference_category,
  pairwise_difference_scale = 1,
  main_difference_scale = 1,
  pairwise_difference_prior = c("Bernoulli", "Beta-Bernoulli"),
  main_difference_prior = c("Bernoulli", "Beta-Bernoulli"),
  pairwise_difference_probability = 0.5,
  main_difference_probability = 0.5,
  pairwise_beta_bernoulli_alpha = 1,
  pairwise_beta_bernoulli_beta = 1,
  main_beta_bernoulli_alpha = 1,
  main_beta_bernoulli_beta = 1,
  interaction_scale = 2.5,
  threshold_alpha = 0.5,
  threshold_beta = 0.5,
  iter = 10000,
  burnin = 500,
  na.action = c("listwise", "impute"),
  save = FALSE,
  display_progress = TRUE
)

Arguments

Details

In the first group, the pairwise interactions between the variables i and j are modeled as

\sigma_{\text{ij}} = \theta_{\text{ij}} + \delta_{\text{ij}} / 2,

and in the second group as

\sigma_{\text{ij}} = \theta_{\text{ij}} - \delta_{\text{ij}} / 2,

The pairwise interaction parameter \theta_{\text{ij}} denotes an overall effect that is considered nuisance, and attention is focused on the pairwise difference parameter \delta_{\text{ij}}, which reflects the difference in the pairwise interaction between the two groups.

The bgmCompare function supports two types of ordinal variables, which can be mixed. The default ordinal variable introduces a threshold parameter for each category except the lowest category. For this variable type, the threshold parameter for variable i, category c, is modeled as

\mu_{\text{ic}} = \tau_{\text{ic}} + \epsilon_{\text{ic}} / 2,

in the first group and in the second group as

\mu_{\text{ic}} = \tau_{\text{ic}} - \epsilon_{\text{ic}} / 2,

The category threshold parameter \tau_{\text{ic}} denotes an overall effect that is considered nuisance, and attention is focused on the threshold difference parameter \epsilon_{\text{ic}}, which reflects the difference in threshold of for variable i, category c between the two groups.

The Blume-Capel ordinal variable assumes that there is a specific reference category, such as “neutral” in a Likert scale, and responses are scored according to their distance from this reference category. In the first group, the threshold parameters are modelled as

\mu_{\text{ic}} = (\tau_{\text{i1}} + \epsilon_{\text{i1}} / 2) \times \text{c} + (\tau_{\text{i2}} + \epsilon_{\text{i2}} / 2) \times (\text{c} - \text{r})^2,

and in the second groups as

\mu_{\text{ic}} = (\tau_{\text{i1}} - \epsilon_{\text{i1}} / 2) \times \text{c} + (\tau_{\text{i2}} - \epsilon_{\text{i2}} / 2) \times (\text{c} - \text{r})^2.

The linear and quadratic category threshold parameters \tau_{\text{i1}} and \tau_{\text{i2}} denote overall effects that are considered nuisance, and attention is focused on the two threshold difference parameters \epsilon_{\text{i1}} and \epsilon_{\text{i2}}, which reflect the differences in the quadratic model for the variable i between the two groups.

Bayesian variable selection is used to model the presence or absence of the difference parameters \delta and \epsilon, which allow us to assess parameter differences between the two groups. Independent spike and slab priors are specified for these difference parameters. The spike and slab priors use binary indicator variables to select the difference parameters, assigning them a diffuse Cauchy prior with an optional scaling parameter if selected, or setting the difference parameter to zero if not selected.

The function offers two models for the probabilistic inclusion of parameter differences:

• Bernoulli Model: This model assigns a fixed probability of selecting a parameter difference, treating them as independent events. A probability of 0.5 indicates no preference, giving equal prior weight to all configurations.

• Beta-Bernoulli Model: Introduces a beta distribution prior for the inclusion probability that models the complexity of the configuration of the difference indicators. When the alpha and beta shape parameters of the beta distribution are set to 1, the model assigns the same prior weight to the number of differences present (i.e., a configuration with two differences or with four differences is a priori equally likely).

Inclusion probabilities can be specified for pairwise interactions with pairwise_difference_probability and for category thresholds with threshold_difference_probability.

The pairwise interaction parameters \theta, the category threshold parameters \tau, and, in the not yet implemented paired-samples designs, the between-sample interactions \omega are considered nuisance parameters that are common to all models. The pairwise interaction parameters \theta and the between-sample interactions \omega are assigned a diffuse Cauchy prior with an optional scaling parameter. The exponent of the category threshold parameters \tau are assigned beta-prime distribution with optional scale values.

Value

If save = FALSE (the default), the result is a list of class “bgmCompare” containing the following matrices:

• indicator: A matrix with p rows and p columns containing the posterior inclusion probabilities of the differences in pairwise interactions on the off-diagonal and the posterior inclusion probabilities of the differences in category thresholds on the diagonal.

• difference_pairwise: A matrix with p rows and p columns, containing model-averaged posterior means of the differences in pairwise interactions.

• difference_threshold: A matrix with p rows and max(m) columns, containing model-averaged posterior means of the differences in category thresholds.

• interactions: A matrix with p rows and p columns, containing posterior means of the nuisance pairwise interactions.

• thresholds: A matrix with p rows and max(m) columns containing the posterior means of the nuisance category thresholds. In the case of “blume-capel” variables, the first entry is the parameter for the linear effect and the second entry is the parameter for the quadratic effect, which models the offset to the reference category.

If save = TRUE, the result is a list of class “bgmCompare” containing the following matrices:

• indicator_pairwise: A matrix with iter rows and p * (p - 1) / 2 columns containing the inclusion indicators for the differences in pairwise interactions from each iteration of the Gibbs sampler.

• difference_pairwise: A matrix with iter rows and p * (p - 1) / 2 columns, containing parameter states for the differences in pairwise interactions from each iteration of the Gibbs sampler.

• indicator_threshold: A matrix with iter rows and sum(m) columns, containing the inclusion indicators for the differences in category thresholds from each iteration of the Gibbs sampler.

• difference_threshold: A matrix with iter rows and sum(m) columns, containing the parameter states for the differences in category thresholds from each iteration of the Gibbs sampler.

• interactions: A matrix with iter rows and p * (p - 1) / 2 columns, containing parameter states for the nuisance pairwise interactions in each iteration of the Gibbs sampler.

• thresholds: A matrix with iter rows and sum(m) columns, containing parameter states for the nuisance category thresholds in each iteration of the Gibbs sampler.

Column averages of these matrices provide the model-averaged posterior means.

In addition to the results of the analysis, the output lists some of the arguments of its call. This is useful for post-processing the results.

Extractor Functions.

Description

Extractor Functions.

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)

## 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)

extract_category_thresholds(bgms_object)

extract_pairwise_difference.bgmCompare(bgms_object)

extract_main_difference.bgmCompare(bgms_object)

extract_edge_indicators(bgms_object)

extract_pairwise_thresholds(bgms_object)

Arguments

Details

Extract results from bgm objects in a safe way. Mainly intended for developers of packages that build on top of the bgms package.

Sample observations from the ordinal MRF

Description

This function samples states from the ordinal MRF using a Gibbs sampler. The Gibbs sampler is initiated with random values from the response options, after which it proceeds by simulating states for each variable from a logistic model 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 default option assumes that the category thresholds are free, except that the first threshold is set to zero for identification. The user then only needs to specify the thresholds for the remaining response categories. This option is useful for any type of ordinal variable and gives the user the most freedom in specifying their model.

The Blume-Capel option is specifically designed for ordinal variables that have a special type of reference_category category, such as the neutral category in a Likert scale. The Blume-Capel model specifies the following quadratic 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 trend across categories (increasing threshold values if \alpha > 0 and decreasing threshold values if \alpha <0), if \beta < 0, it offers an increasing penalty for responding in a category further away from the reference_category category r, while \beta > 0 suggests a preference for responding in the reference_category category.

Value

A no_states by no_variables matrix of simulated states of the ordinal MRF.

Examples

# Generate responses from a network of five binary and ordinal variables.
no_variables = 5
no_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] = .25
Interactions = 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 = 5
no_categories = 4

Interactions = matrix(0, nrow = no_variables, ncol = no_variables)
Interactions[2, 1] = Interactions[4, 1] = Interactions[3, 2] =
  Interactions[5, 2] = Interactions[5, 4] = .25
Interactions = Interactions + t(Interactions)

Thresholds = matrix(NA, no_variables, no_categories)
Thresholds[, 1] = -1
Thresholds[, 2] = -1
Thresholds[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 bgms objects

Description

Used to prevent bgms output cluttering the console.

Usage

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

Arguments

Print method for bgms objects

Description

Used to prevent bgms output cluttering the console.

Usage

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

Arguments