Bayesian hypothesis testing for Gaussian graphical models: Conditional independence and order constraints

Abstract

Gaussian graphical models (GGM; partial correlation networks) have become increasingly popular in the social and behavioral sciences for studying conditional (in)dependencies between variables. In this work, we introduce exploratory and confirmatory Bayesian tests for partial correlations. For the former, we first extend the customary GGM formulation that focuses on conditional dependence to also consider the null hypothesis of conditional independence for each partial correlation. Here a novel testing strategy is introduced that can provide evidence for a null, negative, or positive effect. We then introduce a test for hypotheses with order constraints on partial correlations. This allows for testing theoretical and clinical expectations in GGMs. The novel matrix−F prior distribution is described

The Network Constellation of Personality and Substance Use: Evolution from Early to Late Adolescence

“…The first step involved constructing an adjacency matrix of pairwise conditional relations among the set of items. We estimated the network structure using the Bayesian estimation for a Gaussian graphical model using the BGGM package in r statistical environment (Williams, 2018; Williams & Mulder, 2019). In this model, edges represent partial correlations between nodes, which means an edge depicts the association between two nodes controlling for the associations among all other nodes in the network.…”

“…In this model, edges represent partial correlations between nodes, which means an edge depicts the association between two nodes controlling for the associations among all other nodes in the network. The BGGM has several advantages such as providing edgewise credible intervals from the posterior distributions as well as the possibility of the direct comparison between networks across samples that incorporates uncertainty within the Bayesian framework (Jones, Williams, & McNally, 2019; Williams & Mulder, 2019). To evaluate the accuracy of partial correlation estimates, we evaluated the credible intervals from the posterior distributions and identified nodes linked with cannabis/alcohol use with a 95% credible interval that does not include zero.…”

“…In our case, KLD can be considered as a distance measure between the expected networks of different time points, conditional on the observed data. The lower bound assumes equal network structures across time points (Williams, 2018; Williams & Mulder, 2019). In line with the aims of the current study, for nodewise and edgewise comparisons, we only focused on alcohol use and cannabis use.…”

“…Cannabis and alcohol are the most used substances among adolescents (Lipari, Hedden, & Hughes, 2013). Early onset of cannabis/alcohol use is associated with a range of negative consequences including subsequent dependence (Rioux et al, 2018) and polydrug use (Secades–Villa, Garcia–Rodríguez, Jin, Wang, & Blanco, 2015), cognitive deficits (Castellanos–Ryan et al, 2017; Morin et al, 2018), and psychotic–like experiences (Bourque, Afzali, & Conrod, 2018; Bourque, Afzali, O'Leary–Barrett, & Conrod, 2017). Studies of the personality correlates of adolescent substance use have shown promising results in terms of the development and implementation of targeted prevention/intervention strategies (Conrod et al, 2013; Conrod, O'Leary–Barrett, Massé, Stewart, & Séguin, 2017; Teesson et al, 2017).…”

The case for formal methodology in scientific reform

“…If inferential statistics are employed for the purposes of data exploration, we can prioritize minimizing the probability of failing to reject a false null hypothesis ( Goeman et al, 2011 ; Jaeger and Halliday, 1998 ) as opposed to minimizing false positives because priority is given to not missing true discoveries. Nonetheless, other methods than hypothesis testing are often more closely associated with EDA due to their flexibility in revealing patterns, such as graphical evaluation of data ( Behrens, 1997 ; Tukey, 1980 ), exploratory factor analysis ( Behrens, 1997 ; Haig, 2005 ), principal components regression ( Massy, 1965 ), and Bayesian methods to generate EDA graphs ( Gelman, 2003, 2004 ; Williams and Mulder, 2020 ).…”