Communality ($h_i^2={\sum }_j{L}_{ij}^2$)

The communality is the variance of the shared-factor contribution to variable $i$. In an orthogonal factor model, $\mathrm{Var}(X_i)=h_i^2+{\psi }_i$, where ${\psi }_i$ is its specific variance. For standardized variables, $h_i^2\le 1$. It measures variance shared through the modeled factors, not variance in a chosen principal component.