59: Statistical Inference for Latent Space Model on Network data with Edge Covariates

Music City Center 

Latent space models (LSMs) provide a powerful framework for analyzing network data by embedding nodes in a latent space. Incorporating covariate information via edge covariates is a natural extension that enhances the practical utility of such models. Prior work has shown that effective estimation under this setting can be achieved using maximum likelihood estimators (MLEs). However, the asymptotic normality of the estimators for the edge effect remains unknown, making valid statistical inference challenging. In this work, we establish theoretical guarantees for MLEs under this setting, including consistency and asymptotic normality. Through extensive numerical simulations, we demonstrate that our proposed method enables valid statistical inference for the edge effect. These findings contribute to the statistical methodology for LSMs, providing a principled framework for parameter estimation and inference in network models with edge covariates.

latent space models

maximum likelihood inference

network with edge covariates 

Section on Statistical Learning and Data Science