Bayes factor
Definition
Bayes factor is a statistical measure used to quantify evidence for or against conditional independence between pairs of variables in a network model. In Bayesian network psychometrics, a specific form called the inclusion Bayes factor is derived through Bayesian model averaging and requires researchers to specify prior distributions on both the network structure and the edge weight parameters. The sensitivity of this measure to those prior specifications is substantial: even small changes in the scale of the prior on partial correlations can markedly alter the inclusion Bayes factor's capacity to distinguish between the presence and absence of an edge. Unlike frequentist approaches, which cannot differentiate absence of evidence from evidence of absence, the inclusion Bayes factor directly addresses conditional independence testing in Markov Random Field models applied to ordinal and binary psychological data.
Sources: Sekulovski et al. (2024)
Related Terms
- network psychometrics (1 shared article)
- Bayesian model averaging (1 shared article)
- Bayesian variable selection (1 shared article)
- Markov random fields (1 shared article)
- prior sensitivity (1 shared article)
Applications
Bayes Factor and Prior Distribution
The inclusion Bayes factor's values are directly shaped by two sets of prior distributions: one placed on the network structure and another on the edge weight parameters. Simulation studies examining ordinal Markov Random Field models show that the scale of the prior on partial correlations is particularly consequential, with even modest variations producing substantial shifts in the evidence the Bayes factor registers for or against a given edge.
Sources: Sekulovski et al. (2024)
Bayes Factor and Conditional Independence Testing
Conditional independence testing in network psychometrics requires a method capable of distinguishing genuine absence of an edge from mere insufficient evidence for one. The inclusion Bayes factor addresses this directly by quantifying evidence for conditional independence between pairs of variables after controlling for all remaining variables in the network, an advance over frequentist Lasso-based approaches that conflate these two situations.
Sources: Sekulovski et al. (2024)
Bayes Factor and Bayesian Model Averaging
The inclusion Bayes factor is constructed through Bayesian model averaging, which integrates over uncertainty about the network structure rather than committing to a single structure a priori. This approach requires specifying which edge weight parameters receive a prior distribution and which are fixed to zero, depending on the configuration of edges under consideration in the ordinal Markov Random Field.
Sources: Sekulovski et al. (2024)
