Latent Position-Based Modeling of Parameter Heterogeneity

This paper proposes to use the Generalized Random Dot Product Graph model and the underlying latent positions to model parameter heterogeneity. We discuss how the Stochastic Block Model can be directly applied to model individual parameter heterogeneity. We also develop a new procedure to model pairwise parameter heterogeneity requiring the number of distinct latent distances between unobserved communities to be low. It is proven that, asymptotically, the heterogeneity pattern can be completely recovered. Additionally, we provide three test statistics for the assumption on the number of distinct latent distances. The proposed methods are illustrated using data on a household microfinance program and the S&P 500 component stocks.