Test Dyadic Associations with QAP
Use label permutations to compare aligned relationship matrices while respecting the dependence created when many dyads share the same actors.
Method sources
By the end of this tutorial
- 1Recognize why ordinary independent-observation tests are unsafe for dyadic matrices.
- 2Align outcome and predictor matrices on the same actors and direction.
- 3Interpret a QAP coefficient, permutation distribution, and evidence boundary together.
SNA
Network specification
Analysis scenario
A project team asks whether students who exchange study advice also collaborate on assignments. Both relations involve the same class, so dyads that share a student are not independent observations.
Nodes
Students who were eligible to report both advice and collaboration ties.
Ties
Two aligned directed matrices record advice seeking and assignment collaboration between the same ordered pairs.
Network type
Two one-mode, directed, binary networks on an identical, consistently ordered node set.
Step-by-step tutorial
Align the matrices
Create one row and column order for the shared actor set, then reorder every matrix to match it. Decide how to treat diagonals, missing dyads, direction, and any actors present in only one source.
Checkpoint
The same cell in every matrix refers to the same ordered pair, and missingness is never silently converted to zero.
State the dyadic hypothesis
Specify the outcome matrix, predictor matrix, expected direction, and covariate matrices before analysis. A simple example asks whether advice ties are more likely where collaboration ties exist.
Checkpoint
The hypothesis names the relation being explained and distinguishes it from actor attributes or network controls.
Permute actor labels
Calculate the observed correlation or regression coefficient, then repeatedly permute rows and matching columns together. This preserves each permuted network's internal structure while breaking its alignment with the other matrix.
Checkpoint
Rows and columns move as a pair, the number of permutations is documented, and a random seed supports reproduction.
Report effect and uncertainty
Compare the observed statistic with the permutation distribution. Report the coefficient, permutation-based probability, matrix definitions, controls, permutation count, and sensitivity to direction or missing-data choices.
Checkpoint
The write-up treats QAP as evidence of dyadic association, not proof that one relationship caused the other.
Interpret with care
A positive observed coefficient means aligned dyads with stronger or present predictor ties tend to have stronger or present outcome ties. The permutation result asks how unusual that alignment is when actor labels are reassigned while network structure is retained.
QAP addresses a specific dependence problem, but it does not repair weak measurement, omitted relational processes, temporal ambiguity, or a mismatched boundary. Results can change when matrices use different time windows, tie definitions, or missing-data rules.