A note on nodewise network estimation

Psychometric network estimation often relies on 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 are averaged to obtain the edge weight (i.e., the partial association). The nodewise approach has been shown to reveal the true graph structure for multivariate normally distributed variables. However, the regression coefficients are scaled differently than the partial correlations, and therefore their strength may differ. We show that when the correlations of the two predictors with the control variables are different, the averaged regression coefficients are 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 propose a corrected aggregation of the regression weights by taking the square root of the multiplied regression weights. The corrected parameter can recover the true network structure and edge weights for both standardized and unstandardized variables.