A Trimming Estimator for the Latent-Diffusion-Observed-Adoption Model

TL;DR

This paper introduces a trimming estimator for latent diffusion models in networks, enabling approximate maximum likelihood estimation despite computational challenges due to unobserved diffusion processes.

Contribution

It proposes a novel trimming estimator that simplifies the estimation of complex latent diffusion models with limited agent trimming, improving computational feasibility.

Findings

Estimator nearly identifies the true likelihood peak

Allows estimation with up to one-third agent trimming

Addresses computational infeasibility in multi-round diffusion models

Abstract

Network diffusion models are applicable to many socioeconomic interactions, yet network interaction is hard to observe or measure. Whenever the diffusion process is unobserved, the number of possible realizations of the latent matrix that captures agents' diffusion statuses grows exponentially with the size of network. Due to interdependencies, the log likelihood function can not be factorized in individual components. As a consequence, exact estimation of latent diffusion models with more than one round of interaction is computationally infeasible. In the present paper, I propose a trimming estimator that enables me to establish and maximize an approximate log likelihood function that almost exactly identifies the peak of the true log likelihood function whenever no more than one third of eligible agents are subject to trimming.