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‎README.md‎

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[![Total](https://cranlogs.r-pkg.org/badges/grand-total/bgms)](https://cran.r-project.org/package=bgms)
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# bgms: Bayesian Analysis of Networks of Binary and/or Ordinal Variables
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# bgms <a href="https://bayesiangraphicalmodeling.com"><img src="inst/bgms_sticker.svg" height="200" align="right" /></a>
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<a href="https://bayesiangraphicalmodeling.com"><img src="inst/bgms_sticker.svg" height="200" align="right" /></a>
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**Bayesian analysis of graphical models with binary and ordinal
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variables**
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The **bgms** package implements Bayesian estimation and model comparison
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for **ordinal Markov random fields (MRFs)**, graphical models that
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``` r
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browseVignettes("bgms")
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#> No vignettes found by browseVignettes("bgms")
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```
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## Why use Markov Random Fields?
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Multivariate analysis using graphical models has received much attention
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in the recent psychological and psychometric literature (Contreras et
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al., 2019; Marsman & Rhemtulla, 2022; Robinaugh et al., 2020). Most of
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these graphical models are Markov Random Field (MRF) models, whose graph
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structure reflects the partial associations between variables
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(Kindermann & Snell, 1980). In these models, a missing edge between two
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variables in the network implies that these variables are independent,
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given the remaining variables (Lauritzen, 2004). In other words, the
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remaining variables of the network fully account for the potential
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association between the unconnected variables.
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## Why use a Bayesian approach to analyze the MRF?
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Testing the structure of the MRF in a one-sample design requires us to
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determine the plausibility of the opposing hypotheses of conditional
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dependence and conditional independence. That is, how plausible is it
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that the observed data come from a network with a structure that
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includes the edge between two variables compared to a network structure
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that excludes that edge? Similarly, testing for group differences in the
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MRF in an independent-samples design requires us to determine the
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plausibility of the opposing hypotheses of parameter difference and
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parameter equivalence. That is, how plausible is it that the observed
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data come from MRFs with differences in specific edge weights or
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threshold parameters compared to MRFs that do not differ in these
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parameter?
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Frequentist approaches are limited in this respect because they can only
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reject, not support, null hypotheses of conditional independence or
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parameter equivalence. This leads to the problem that if an edge is
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excluded, we do not know whether this is because the edge is absent in
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the population or because we do not have enough data to reject the null
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hypothesis of independence. Similarly, if a difference is excluded, we
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do not know whether this is because there is no difference in the
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parameter between the different groups or because we do not have enough
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data to reject the null hypothesis of parameter equivalence.
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To avoid this problem, we will advocate a Bayesian approach using Bayes
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factors. In one-sample designs, the inclusion Bayes factor (Huth et al.,
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2023; Sekulovski et al., 2024) allows us to quantify how much the data
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support both conditional dependence -<em>evidence of edge
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presence</em> - or conditional independence -<em>evidence of edge
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absence</em>. It also allows us to conclude that there is limited
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support for either hypothesis - an <em>absence of evidence</em>. In
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independent-sample designs, they can be used to quantify how much the
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data support the hypotheses of parameter difference and equivalence. The
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output of the <strong>bgm</strong> and <strong>bgmCompare</strong>
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functions can be used to estimate these inclusion Bayes factors.
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Graphical models or networks have become central in recent psychological
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and psychometric research (Contreras et al., 2019; Marsman & Rhemtulla,
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2022; Robinaugh et al., 2020). Most are **Markov random field (MRF)**
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models, where the graph structure reflects partial associations between
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variables (Kindermann & Snell, 1980).
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In an MRF, a missing edge between two variables implies **conditional
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independence** given the rest of the network (Lauritzen, 2004). In other
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words, the remaining variables fully explain away any potential
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association between the unconnected pair.
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## Why use a Bayesian approach?
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When analyzing an MRF, we often want to compare competing hypotheses:
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- **Edge presence vs. edge absence** (conditional dependence
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vs. independence) in one-sample designs.
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- **Parameter difference vs. parameter equivalence** in
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independent-sample designs.
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Frequentist approaches are limited in such comparisons: they can reject
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a null hypothesis, but they cannot provide evidence *for* it.
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As a result, when an edge or difference is excluded, it remains unclear
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whether this reflects true absence or simply insufficient power.
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Bayesian inference avoids this problem.
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Using **inclusion Bayes factors** (Huth et al., 2023; Sekulovski et al.,
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2024), we can quantify evidence in both directions:
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- **Evidence of edge presence** vs. **evidence of edge absence**, or
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- **Evidence of parameter difference** vs. **evidence of parameter
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equivalence**.
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This makes it possible not only to detect structure and group
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differences, but also to conclude when there is an *absence of
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evidence*.
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## Installation
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‎Readme.Rmd‎

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[![Total](https://cranlogs.r-pkg.org/badges/grand-total/bgms)](https://cran.r-project.org/package=bgms)
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<!-- badges: end -->
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# bgms: Bayesian Analysis of Networks of Binary and/or Ordinal Variables
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<a href="https://bayesiangraphicalmodeling.com"><img src="inst/bgms_sticker.svg" height="200" align="right" /></a>
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# bgms <a href="https://bayesiangraphicalmodeling.com"><img src="inst/bgms_sticker.svg" height="200" align="right" /></a>
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**Bayesian analysis of graphical models with binary and ordinal variables**
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The **bgms** package implements Bayesian estimation and model comparison for
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**ordinal Markov random fields (MRFs)**, graphical models that represent
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## Why use Markov Random Fields?
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Multivariate analysis using graphical models has received much attention in the recent psychological and psychometric literature [@RobinaughEtAl_2020; @MarsmanRhemtulla_2022_SIintro; @ContrerasEtAl_2019]. Most of these graphical models are Markov Random Field (MRF) models, whose graph structure reflects the partial associations between variables [@KindermannSnell1980]. In these models, a missing edge between two variables in the network implies that these variables are independent, given the remaining variables [@Lauritzen2004]. In other words, the remaining variables of the network fully account for the potential association between the unconnected variables.
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Graphical models or networks have become central in recent psychological and psychometric research [@RobinaughEtAl_2020; @MarsmanRhemtulla_2022_SIintro; @ContrerasEtAl_2019]. Most are **Markov random field (MRF)** models, where the graph structure reflects partial associations between variables [@KindermannSnell1980].
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In an MRF, a missing edge between two variables implies **conditional independence** given the rest of the network [@Lauritzen2004]. In other words, the remaining variables fully explain away any potential association between the unconnected pair.
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## Why use a Bayesian approach?
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When analyzing an MRF, we often want to compare competing hypotheses:
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- **Edge presence vs. edge absence** (conditional dependence vs. independence) in one-sample designs.
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- **Parameter difference vs. parameter equivalence** in independent-sample designs.
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## Why use a Bayesian approach to analyze the MRF?
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Frequentist approaches are limited in such comparisons: they can reject a null hypothesis, but they cannot provide evidence *for* it.
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As a result, when an edge or difference is excluded, it remains unclear whether this reflects true absence or simply insufficient power.
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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 an 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 MRFs with differences in specific edge weights or threshold parameters compared to MRFs that do not differ in these parameter?
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Bayesian inference avoids this problem.
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Using **inclusion Bayes factors** [@HuthEtAl_2023_intro; @SekulovskiEtAl_2024], we can quantify evidence in both directions:
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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 different groups or because we do not have enough data to reject the null hypothesis of parameter equivalence.
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- **Evidence of edge presence** vs. **evidence of edge absence**, or
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- **Evidence of parameter difference** vs. **evidence of parameter equivalence**.
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To avoid this problem, we will advocate a Bayesian approach using Bayes factors. In one-sample designs, the inclusion Bayes factor [@HuthEtAl_2023_intro; @SekulovskiEtAl_2024] allows us to quantify how much the data support both conditional dependence -<em>evidence of edge presence</em> - or conditional independence -<em>evidence of edge absence</em>. It also allows us to conclude that there is limited support for either hypothesis - an <em>absence of evidence</em>. In independent-sample designs, they can be used to quantify how much the data support the hypotheses of parameter difference and equivalence. The output of the <strong>bgm</strong> and <strong>bgmCompare</strong> functions can be used to estimate these inclusion Bayes factors.
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This makes it possible not only to detect structure and group differences, but also to conclude when there is an *absence of evidence*.
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## Installation
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