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| Quadratic Assignment Procedure× | MRQAP Network Regression× | |
|---|---|---|
| Field | Sociology | Sociology |
| Family≠ | Process / pipeline | Regression model |
| Year of origin≠ | 1976 (QAP); 1988 (network application) | 1988 (MRQAP); 2007 (double-semipartialing test) |
| Originator≠ | Lawrence Hubert & James Schultz; David Krackhardt | David Krackhardt; David Dekker, David Krackhardt & Tom Snijders |
| Type≠ | Permutation-based test of association between two matrices | Permutation-based multiple regression for dyadic (matrix) outcomes |
| Seminal source | Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks, 10(4), 359–381. DOI ↗ | Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks, 10(4), 359–381. DOI ↗ |
| Aliases | QAP correlation, QAP permutation test, matrix permutation test, Hubert-Schultz QAP | MRQAP, multiple regression QAP, Dekker double-semipartialing, QAP regression |
| Related | 4 | 4 |
| Summary≠ | The quadratic assignment procedure (QAP) is a permutation-based method for testing the association between two relational matrices measured on the same set of actors — for example, whether who advises whom is correlated with who is friends with whom. Because the dyads in a network are not independent, ordinary correlation and regression give invalid p-values; QAP fixes this by comparing the observed matrix correlation to a reference distribution generated by randomly relabeling the nodes of one matrix many times. | Multiple regression quadratic assignment procedure (MRQAP) extends QAP to the regression setting: it predicts a dependent relational matrix from several independent relational matrices on the same actors — for example, modeling who collaborates with whom as a function of who is co-located, who shares a department, and who has prior friendship. Coefficients are estimated by ordinary least squares on the vectorized matrices, but significance is assessed by permutation, because dyadic dependence invalidates the standard regression standard errors. |
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