Partial correlation networks have emerged as an increasingly popular model for studyingmental disorders. Although conditional independence is a fundamental concept in networkanalysis, which corresponds to the null hypothesis, the focus is typically to detect and thenvisualize non-zero partial correlations (i.e., the “edges” connecting nodes) in a graph. As aresult, it may be tempting to interpret a missing edge as providing evidence for itsabsence—analogously to misinterpreting a non-significant p-value. In this work, we firstestablish that a missing edge is incorrectly interpreted as providing evidence for conditionalindependence, with examples spanning from substantive applications to tutorials thatinstruct researchers to misinterpret their networks. We then go beyond misguided“inferences” and establish that null associations are interesting in their own right. In thefollowing section, three illustrative examples are provided that employ Bayesian hypothesistesting to formally evaluate the null hypothesis, including a reanalysis of twopsychopathology networks, confirmatory testing to determine whether a particularpost-traumatic stress disorder symptom is disconnected from the network, and attenuationdue to correcting for covariates. Our results shed light upon conditionally independentsymptoms and demonstrate that a missing edge does not necessarily correspond toevidence for the null hypothesis. These findings are accompanied with a simulation studythat provides insights into the sample size needed to accurately detect null relations. Weconclude with implications for both clinical to theoretical inquiries.
On Accepting the Null Hypothesis of Conditional Independence in Partial Correlation Networks: A Bayesian Analysis