Asymptotic theory of the quadratic assignment procedure for dyadic data analysis
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916637755572224 |
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| author | Shi, Lei Ding, Peng |
| author_facet | Shi, Lei Ding, Peng |
| contents | The quadratic assignment procedure (QAP) is a popular tool for analyzing dyadic data in medical and social sciences. To test the association between two dyadic measurements represented by two symmetric matrices, QAP calculates the p-value by permuting the units, or equivalently, by permuting the rows and columns of one matrix in the same way. Its extension to the regression setting, known as the multiple regression QAP, has also gained popularity, especially in psychometrics. However, the statistics theory for QAP has not been fully established in the literature. We fill the gap in this paper. We formulate the network models underlying various QAPs. We derive (a) the asymptotic sampling distributions of some canonical test statistics and (b) the corresponding asymptotic permutation distributions induced by QAP under strong and weak null hypotheses. Task (a) relies on applying the theory of U-statistics, and task (b) relies on applying the theory of double-indexed permutation statistics. The combination of tasks (a) and (b) provides a relatively complete picture of QAP. Overall, our asymptotic theory suggests that using properly studentized statistics in QAP is a robust choice in that it is finite-sample exact under the strong null hypothesis and preserves the asymptotic type one error rate under the weak null hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic theory of the quadratic assignment procedure for dyadic data analysis Shi, Lei Ding, Peng Methodology 62K15, 62J05, 62G05 The quadratic assignment procedure (QAP) is a popular tool for analyzing dyadic data in medical and social sciences. To test the association between two dyadic measurements represented by two symmetric matrices, QAP calculates the p-value by permuting the units, or equivalently, by permuting the rows and columns of one matrix in the same way. Its extension to the regression setting, known as the multiple regression QAP, has also gained popularity, especially in psychometrics. However, the statistics theory for QAP has not been fully established in the literature. We fill the gap in this paper. We formulate the network models underlying various QAPs. We derive (a) the asymptotic sampling distributions of some canonical test statistics and (b) the corresponding asymptotic permutation distributions induced by QAP under strong and weak null hypotheses. Task (a) relies on applying the theory of U-statistics, and task (b) relies on applying the theory of double-indexed permutation statistics. The combination of tasks (a) and (b) provides a relatively complete picture of QAP. Overall, our asymptotic theory suggests that using properly studentized statistics in QAP is a robust choice in that it is finite-sample exact under the strong null hypothesis and preserves the asymptotic type one error rate under the weak null hypothesis. |
| title | Asymptotic theory of the quadratic assignment procedure for dyadic data analysis |
| topic | Methodology 62K15, 62J05, 62G05 |
| url | https://arxiv.org/abs/2411.00947 |