User modeling plays an important role in delivering customized web services to the users and improving their engagement. However, most user models in the literature do not explicitly consider the temporal behavior of users. More recently, continuous-time user modeling has gained considerable attention and many user behavior models have been proposed based on temporal point processes. However, typical point process based models often considered the impact of peer influence and content on the user participation and neglected other factors. Gamification elements, are among those factors that are neglected, while they have a strong impact on user participation in online services. In this paper, we propose interdependent multi-dimensional temporal point processes that capture the impact of badges on user participation besides the peer influence and content factors. We extend the proposed processes to model user actions over the community based question and answering websites, and propose an inference algorithm based on Variational-EM that can efficiently learn the model parameters. Extensive experiments on both synthetic and real data gathered from Stack Overflow show that our inference algorithm learns the parameters efficiently and the proposed method can better predict the user behavior compared to the alternatives.