Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independent given the rest of the network variables. This conditional independence structure is a gateway to understanding the causal structure underlying psychological processes. Thus, it is crucial to have an appropriate method for evaluating conditional independence and dependence hypotheses. Bayesian approaches to testing such hypotheses allow researchers to differentiate between absence of evidence and evidence of absence of connections (edges) between pairs of variables in a network. Three Bayesian approaches to assessing conditional independence have been proposed in the network psychometrics literature. We believe that their theoretical foundations are not widely known, and therefore we provide a conceptual review of the proposed methods and highlight their strengths and limitations through a simulation study. We also illustrate the methods using an empirical example with data on Dark Triad Personality. Finally, we provide recommendations on how to choose the optimal method and discuss the current gaps in the literature on this important topic.
Keywords: Bayes factor; Bayesian model averaging; Conditional independence; Markov random fields.