Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions

Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions. Dekker, D., Krackhardt, D., & Snijders, T. A. B. Psychometrika, 72(4):563–581, December, 2007.

Paper doi abstract bibtex

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 semipartialing”, 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{dekkerSensitivityMRQAPTests2007,
	title = {Sensitivity of {MRQAP} {Tests} to {Collinearity} and {Autocorrelation} {Conditions}},
	volume = {72},
	copyright = {https://www.cambridge.org/core/terms},
	issn = {0033-3123, 1860-0980},
	url = {https://www.cambridge.org/core/product/identifier/S0033312300022444/type/journal_article},
	doi = {10.1007/s11336-007-9016-1},
	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 semipartialing”, 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.},
	language = {en},
	number = {4},
	urldate = {2025-02-19},
	journal = {Psychometrika},
	author = {Dekker, David and Krackhardt, David and Snijders, Tom A. B.},
	month = dec,
	year = {2007},
	pages = {563--581},
}

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