Statistical Inference in Large Multi-way Networks
arXiv:2512.02203
The paper introduces the Polyads estimator, a method for estimating structural parameters in weighted multi-way networks that handles arbitrary fixed effects without the incidental parameter problem, offering consistency, asymptotic normality, and faster computation than PPML, especially in sparse settings, and demonstrates its use on French health insurance data.
Abstract
We propose the Polyads estimator, a new method to estimate structural parameters in weighted multi-way networks while controlling for rich, arbitrary structures of fixed effects. The method is based on a series of classification tasks and is agnostic to both the number and structure of fixed effects. Unlike full maximum likelihood, our estimator does not suffer from the incidental parameter problem: it is consistent and satisfies a Central Limit Theorem with no asymptotic bias, even when some dimensions of the network are short. For sparsely connected networks, it is also computationally faster than PPML. We provide experimental evidence that our estimator yields more reliable confidence intervals, i.e., better empirical coverage, than PPML and its bias-correction strategies. These improvements hold even under model misspecification and are more pronounced in sparse settings. While PPML remains competitive in dense, low-dimensional data, our approach offers a robust alternative for multi-way models that scales efficiently with sparsity. We apply the method to French health insurance claims data to study how a 2017 physician fee reform affected the geography and gender composition of doctor-patient connections.
Working paper