Semiparametric Modeling and Analysis for Longitudinal Network Data

TL;DR

This paper proposes a semiparametric latent space model for analyzing longitudinal network data, incorporating static and dynamic components, with efficient estimation methods and theoretical guarantees, demonstrated on a bike-sharing dataset.

Contribution

It introduces a novel semiparametric model with efficient estimation techniques and theoretical error bounds for longitudinal network analysis.

Findings

Effective estimation of latent space parameters.

Oracle error bounds established for estimators.

Application to real-world bike-sharing data demonstrates practicality.

Abstract

We introduce a semiparametric latent space model for analyzing longitudinal network data. The model consists of a static latent space component and a time-varying node-specific baseline component. We develop a semiparametric efficient score equation for the latent space parameter by adjusting for the baseline nuisance component. Estimation is accomplished through a one-step update estimator and an appropriately penalized maximum likelihood estimator. We derive oracle error bounds for the two estimators and address identifiability concerns from a quotient manifold perspective. Our approach is demonstrated using the New York Citi Bike Dataset.