Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions

MRQAP (Multiple Regression { Quadratic Assignment Procedure) tests are permutation tests for multiple regression coe±cients for data organized in square matrices instead of vectors. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors. Over the last 15 years, new approaches to permutation tests have been developed. Some of the proposed tests have been found to be substantially more robust against collinearity in the data. Most studies evaluating the performance of permutation tests in linear models for square matrices do not consider the type of structural autocorrelation that is typical for social network data. We present a new permutation method that complements the family of extant tests. Performance of various di®erent approaches to MRQAP tests is evaluated under conditions of row and column autocorrelation in the data as well as collinearity between the variables through an extensive series of simulations.