Nodewise Parameter Aggregation for Psychometric Networks

Psychometric networks can be estimated using nodewise regression to estimate edge weights when the joint distribution is analytically difficult to derive or the estimation is too computationally intensive. The nodewise approach runs generalized linear models with each node as the outcome. Two regression coefficients are obtained for each link, which need to be aggregated to obtain the edge weight (i.e., the conditional association). The nodewise approach has been shown to reveal the true graph structure. However, for continuous variables, the regression coefficients are scaled differently than the partial correlations, and therefore the nodewise approach may lead to different edge weights. Here, the aggregation of the two regression coefficients is crucial in obtaining the true partial correlation. We show that when the correlations of the two predictors with the control variables are different, averaging the regression coefficients leads to an asymptotically biased estimator of the partial correlation. This is likely to occur when a variable has a high correlation with other nodes in the network (e.g., variables in the same domain) and a lower correlation with another node (e.g., variables in a different domain). We discuss two different ways of aggregating the regression weights, which can obtain the true partial correlation: first, multiplying the weights and taking their square root, and second, rescaling the regression weight by the residual variances. The two latter estimators can recover the true network structure and edge weights.