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This paper proposes a new class of innovation diffusion models which are extensions of the standard logistic model, the Bass model, and the Gompertz model for the case when the observed process is the result of the interaction of several unobserved processes, e.g., for the case when the process allows the possibility of repeated use of innovation by each subject of the process over time. In order to check the viability of the models and their ability to adequately describe and predict the process of diffusion of innovations, the time series data of mobile phone subscribers are used in this paper. These time series are employed to compare the performance of the proposed models with the classical innovation diffusion models. Empirical results show that the extended models surpass the classical models, and the examined models have a better performance on real data. [ABSTRACT FROM AUTHOR]