The Fused Graphical Lasso for computing psychological networks

Networks have been recently proposed as plausible models of psychological phenomena in several domains, such as personality psychology and psychopathology. In these fields, nodes represent variables such as cognitions, behaviors, emotions, motivations, and symptoms, and edges represent their pairwise associations. Edge weights are typically estimated using regularized partial correlations, for instance via the graphical lasso. In several situations, it is necessary to compute networks on observations that belong to different classes (e.g., patients vs. controls). Previous studies estimated either a single network for all classes or several networks in each class independently. These strategies may be both suboptimal. The Fused Graphical Lasso (FGL) has been recently proposed for dealing with such situations (Danaher et al., 2014), but it has never been applied to psychology before. FGL allows simultaneously estimating multiple partial correlation networks from observations belonging to different classes. FGL does not assume that the networks are similar, but if similarities are present, they are exploited to improve parameter estimates. This method requires setting two tuning parameters: One is akin to the graphical lasso parameter and controls sparsity, the second one controls the amount of similarity among classes. We developed an R package that implements automatic tuning parameter selection according to information criteria (AIC, BIC, and extended BIC) or relying on k-fold crossvalidation. We present FGL from a theoretical point of view, discuss its performance in simulation studies, and show examples of its applications to personality psychology and psychopathology.