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Description: Bayesian variable selection methods for analyzing the structure of a Markov random field model for a network of binary and/or ordinal variables.
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Copyright: Includes datasets 'ADHD' and 'Boredom', which are licensed under CC-BY 4. See individual data documentation for license and citation.
-[Diagnostics and Spike-and-Slab Summaries](https://bayesian-graphical-modelling-lab.github.io/bgms/articles/diagnostics.html)
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You can also access these directly from R with:
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## Why use Markov Random Fields?
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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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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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-**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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Frequentist approaches are limited in such comparisons: they can reject a null hypothesis, but they cannot provide evidence *for* it. 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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Bayesian inference avoids this problem. Using **inclusion Bayes factors**[@HuthEtAl_2023_intro; @SekulovskiEtAl_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 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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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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