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.
%0 Journal Article
%1 dekker_sensitivity_2007
%A Dekker, David
%A Krackhardt, David
%A Snijders, Tom A. B.
%D 2007
%J Psychometrika
%K analysis analysis, correlation, multiple network permutation, regression, social
%N 4
%P 563--581
%R 10.1007/s11336-007-9016-1
%T Sensitivity of MRQAP tests to collinearity and autocorrelation conditions
%U http://link.springer.com/article/10.1007/s11336-007-9016-1
%V 72
%X 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.
@article{dekker_sensitivity_2007,
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.},
added-at = {2017-01-09T13:57:26.000+0100},
author = {Dekker, David and Krackhardt, David and Snijders, Tom A. B.},
biburl = {https://www.bibsonomy.org/bibtex/2fb5fe09b43c148af7d40c22bb1e9f191/yourwelcome},
doi = {10.1007/s11336-007-9016-1},
interhash = {54e7849870023e5c70835164d17367cf},
intrahash = {fb5fe09b43c148af7d40c22bb1e9f191},
issn = {0033-3123, 1860-0980},
journal = {Psychometrika},
keywords = {analysis analysis, correlation, multiple network permutation, regression, social},
language = {en},
month = dec,
number = 4,
pages = {563--581},
timestamp = {2017-01-09T14:01:11.000+0100},
title = {Sensitivity of {MRQAP} tests to collinearity and autocorrelation conditions},
url = {http://link.springer.com/article/10.1007/s11336-007-9016-1},
urldate = {2014-02-04},
volume = 72,
year = 2007
}