QAP

The relationalstats.qap module provides Quadratic Assignment Procedure models for dyadic relational data.

The first implementation is QAPLogit, a logistic-regression model for binary network outcomes with node-label permutations.

Public API

from relationalstats.qap import QAPLogit

Example:

from relationalstats.datasets import make_qap_toy_data
from relationalstats.qap import QAPLogit

y, x_matrices = make_qap_toy_data()

result = QAPLogit(
    n_permutations=99,
    random_state=42,
    directed=True,
    backend="statsmodels",
).fit(y, x_matrices)

result.to_dataframe()

Backend options

QAPLogit supports two logistic-regression backends.

Backend	Use case	Diagnostics
statsmodels	Default backend for richer model diagnostics	coefficients, standard errors, z-values, backend p-values
sklearn	Faster regularized backend for larger permutation workflows	coefficients only; diagnostic fields are NaN

Backend p-values are retained only as diagnostics. QAP empirical p-values are the primary permutation-based inference output.

For validation against R sna::netlogit, prefer the statsmodels backend because it is closer to a classical logistic-regression workflow.

Documentation

• Formulas
• Validation against R

Methodological scope

QAPLogit is intended for binary dyadic outcomes represented as square matrices.

The model uses:

• a logistic-regression backend for observed coefficients;
• node-label permutations of the dependent matrix;
• plus-one empirical p-values from the permutation distribution.

Backend p-values are retained as diagnostics, but QAP p-values are the primary permutation-based inference output.