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Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions

Published online by Cambridge University Press:  01 January 2025

David Dekker ,
David Krackhardt  and
Tom A. B. Snijders
David Dekker*
Affiliation:
Radboud University Nijmegen
David Krackhardt
Affiliation:
Carnegie Mellon University
Tom A. B. Snijders
Affiliation:
University of Groningen and University of Oxford
*
Requests for reprints should be sent to David Dekker, Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000DR Rotterdam, The Netherlands. E-mail: ddekker@few.eur.nl
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Abstract

Multiple regression quadratic assignment procedures (MRQAP) tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among n objects. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors. We present a new permutation method (called “double semi-partialing”, or DSP) that complements the family of extant approaches to MRQAP tests. We assess the statistical bias (type I error rate) and statistical power of the set of five methods, including DSP, across a variety of conditions of network autocorrelation, of spuriousness (size of confounder effect), and of skewness in the data. These conditions are explored across three assumed data distributions: normal, gamma, and negative binomial. We find that the Freedman–Lane method and the DSP method are the most robust against a wide array of these conditions. We also find that all five methods perform better if the test statistic is pivotal. Finally, we find limitations of usefulness for MRQAP tests: All tests degrade under simultaneous conditions of extreme skewness and high spuriousness for gamma and negative binomial distributions.

Keywords

MRQAPMantel testspermutation testssocial networksnetwork autocorrelationcollinearitydyadic data
Type
Theory and Methods
Information
Psychometrika , Volume 72 , Issue 4 , December 2007 , pp. 563 - 581
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

Special thanks go to Cajo Ter Braak, Philip Hans Franses, Patrick Houweling, Pierre Legendre, three anonymous reviewers, the associate editor, and the editor for comments.

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