Consider inference on a matrix dyadic data, such as predicting future income based on a binary friendship relation among i and j, or a measure of distance between i and j in a hierarchy. The problem is that OLS on the dyadic data matrix will suffer from a problem that looks like autocorrelation – by definition, the dependent variable for i is a function of i’s relations with i and j, and therefore is likely to be correlated with the dependent variable for j. Standard econometric tools like GLS have trouble here, because GLS requires a model of the autocorrelation matrix, and there is often no theoretical basis for assumptions on this matrix when using network data. Using Monte Carlo analysis, Krockhardt shows that the Quadratic Assignment Procedure (developed in the 1960s) gives accurate hypothesis tests no matter the level of autocorrelation.
“Predicting with Networks: Nonparametric Multiple Regression Analysis of Dyadic Data,” D. Krockhardt (1988)