Network estimation and accuracy

MA Matteo Aloi
MR Marianna Rania
EC Elvira Anna Carbone
MC Mariarita Caroleo
GC Giuseppina Calabrò
PZ Paolo Zaffino
GN Giuseppe Nicolò
AC Antonino Carcione
GC Gianluca Lo Coco
CC Carlo Cosentino
CS Cristina Segura-Garcia
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NA was performed using the R (version 3.6.2) qgraph and bootnet packages in accordance with Epskamp and colleagues [47].

The network has been inferred by means of Gaussian Markov random field estimation, applying ‘Least Absolute Shrinkage and Selection Operator’(LASSO) regularization to limit the number of spurious associations [48]. Moreover, the extended Bayesian information criterion (EBIC) [49], a tuning parameter that sets the degree of regularization/penalty applied to sparse correlations, was set to 0.20 in the current study (values between 0 and 0.5 are typically chosen). Network estimation was performed using the estimateNetwork routine of the bootnet package [50].

The centrality of a node is used to infer its influence, or structural importance, in the network. Three main indices estimate the centrality: betweenness (how a node influences the average path between other pairs of nodes); closeness (how a node is indirectly connected to the other nodes); and strength (how a node is directly connected to the other nodes). The centrality Plot function in qgraph was used to calculate indices of centrality.

According to the recommendations of Epskamp et al. [51], in order to assess the internal reliability of the network we calculated the correlation stability (CS) coefficient, which is the maximum proportion of the population that can be dropped so that the correlation between the re-calculated indices of the obtained networks and those of the original network is at least 0.7. It is recommended that the minimum cut-off to consider a network stable is 0.25 for betweenness, closeness and strength [51]. The CS coefficient was computed using case-drop bootstrapping (nboots = 2000). Then we estimated the accuracy of edge-weights by drawing bootstrapped confidence intervals calculated using non-parametric bootstrapping (nboots = 2000). Both for case-drop and non-parametric bootstrapping, network stability analyses were performed using the bootnet function in the bootnet package.

Visual inspection of the network reveals that thicker edges indicate stronger associations between symptoms, with positive associations typically illustrated in blue and negative associations typically represented in red.

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