Influence networks: Bayesian modeling and diffusion

In this article, we make an innovative adaptation of a Bayesian latent space model based on projections in a novel way to analyze influence networks. By appropriately reparameterizing the model, we establish a formal metric for quantifying each individual's influencing capacity and estimating their latent position embedded in a social space. This modeling approach introduces a novel mechanism for simulating the diffusion of an idea based on the estimated latent characteristics. It assumes that each individual takes the following states: Unknown, undecided, supporting, or rejecting an idea. This approach is demonstrated using an influence network from Twitter (now <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi></mml:mrow> </mml:math> ) related to the 2022 Tax Reform in Colombia. An exhaustive simulation exercise is also performed to evaluate the proposed diffusion process.