How missing edges affect estimation and prediction accuracy in the graph-based Poisson process model

Spreading processes in a population, such as the adoption of a novel innovation or product, may be driven by both viral interactions and external factors. The social graph of the population is usually used to model peer-to-peer interactions, but in practice, such graphs are never completely observed. In particular, certain interactions may be missing. We conduct a simulation study to determine how missing interactions affect the inference and predictions of the graph-based Poisson process model introduced by Parviero et al. (2022), modelling both peer-to-peer and external influences. If the social graph is only partly observed, simulations show that parameter estimation will be biased. The external share of the overall cumulative intensity is seen to be overestimated, while the viral share is underestimated. The estimated parameters are seen to increase. Simulations suggest that the bias will be relatively small even for high proportions of missing interactions. In addition, the simulations suggest that resulting predictions are not particularly affected.