Online discussion in form of written comments is a core component of many social media platforms. It has attracted increasing attention from academia, mainly because theories from social sciences can be explored at an unprecedented scale. This interest has led to the development of statistical models which are able to characterize the dynamics of threaded online conversations. In this paper, we review research on statistical modeling of online discussions, in particular, we describe current generative models of the structure and growth of discussion threads. These are parametrized network formation models that are able to generate synthetic discussion threads that reproduce certain features of the real discussions present in different online platforms. We aim to provide a clear overview of the state of the art and to motivate future work in this relevant research field.

This work has been supported by the Spanish Ministry of Economy and Competitiveness under the María de Maeztu Units of Excellence Programme (MDM-2015-0502); the Marie Curie FP7-PEOPLE-2012-COFUND Action (grant agreement no: 600387); and the CIEN LPS-BIGGER project (UCTR150175, IDI-20141259), co-funded by Centro para el Desarrollo Tecnológico Industrial (CDTI) and Fondo Europeo de Desarrollo Regional (FEDER).