Investigation of the Time Series Users’ Reactions on Instagram and Its Statistical Modeling

For the last decade, social networking services (SNS), such as X, Facebook, and Instagram, have become mainstream media for advertising and marketing. In SNS marketing, word-of-mouth among users can spread posted advertising information, which is known as viral marketing. In this study, we first analyzed the time series of user reactions to Instagram posts to clarify the characteristics of user behavior. Second, we modeled these variations using statistical distributions to predict the information diffusion of future posts and to provide some insights into the factors that affect users’ reactions on Instagram using the estimated parameters of the modeling. Our results demonstrate that user reactions have a peak value immediately after posting and decrease drastically and exponentially as time elapses. In addition, modeling with the Weibull distribution is the most suitable for user reactions, and the estimated parameters help identify key factors that influence user reactions.