The likelihood-ratio test for multi-edge network models

TL;DR

This paper demonstrates that the standard chi-squared approximation for likelihood-ratio tests is inadequate for multi-edge network data and proposes a Beta distribution-based correction for more accurate p-value estimation.

Contribution

The authors introduce a Beta distribution approximation for the likelihood-ratio test null-distribution tailored to multi-edge network data, improving statistical inference accuracy.

Findings

Chi-squared approximation is inaccurate for multi-edge networks

Beta distribution provides a better null-distribution approximation

Improved p-value estimation enhances hypothesis testing in complex networks

Abstract

The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio test's null-distribution needs to be modified to accommodate the complexity found in multi-edge network data. When working with independent observations, the p-values of likelihood-ratio tests are approximated using a $\chi^2$ distribution. However, such an approximation should not be used when dealing with multi-edge network data. This type of data is characterized by multiple correlations and competitions that make the standard approximation unsuitable. We provide a solution to the problem by providing a better approximation of the likelihood-ratio test null-distribution through a Beta distribution. Finally, we empirically show that even for a small multi-edge network, the standard $\chi^2$ approximation provides erroneous results, while the proposed Beta approximation yields the correct p-value estimation.