arXiv subjects

Frank W. Marrs

Publications and source records attributed to Frank W. Marrs.

3 recordsLinked to original sources

arXiv2023

Regression of binary network data with exchangeable latent errors

Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models, however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the Probit Exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically-aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

stat.ME↗

arXiv2022

Regression of exchangeable relational arrays

Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms, and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modeled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators -- and ideally the coefficient estimators themselves -- must account for dependence between elements of the array (e.g. relations involving the same actor) and existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. We leverage an exchangeability assumption to derive standard error estimators that pool information across actors and are substantially more accurate than existing estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a data set involving international trade.

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arXiv2019

Inferring Influence Networks from Longitudinal Bipartite Relational Data

Longitudinal bipartite relational data characterize the evolution of relations between pairs of actors, where actors are of two distinct types and relations exist only between disparate types. A common goal is to understand the temporal dependencies, specifically which actor relations incite later actor relations. There are two existing approaches to this problem. The first approach projects the bipartite data in each time period to a unipartite network and uses existing unipartite network models. Unfortunately, information is lost in calculating the projection and generative models for networks obtained through this process are scarce. The second approach represents dependencies using two unipartite \emph{influence networks}, corresponding to the two actor types. Existing models taking this approach are bilinear in the influence networks, creating challenges in computation and interpretation. We propose a novel generative model that permits estimation of weighted, directed influence networks and does not suffer from these shortcomings. The proposed model is linear in the influence networks, permitting inference using off-the-shelf software tools. We prove our estimator is consistent under cases of model misspecification and nearly asymptotically equivalent to the bilinear estimator. We demonstrate the performance of the proposed model in simulation studies and an analysis of weekly international state interactions.

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