Innovation diffusion models incorporating time lag between innovators and imitators adoption

Since time immemorial, managers have been interested in the diffusion of innovations. The philosophy being, if one can better understand how innovations diffuse, one can better predict and manage that diffusion. Innovation diffusion has become highly multifaceted ever since 1969, when the famous Bass model was proposed. Although innovation diffusion modeling has been an area of widespread research in the last 50 years or so, which has resulted in a body of literature, however we consider unfolding and incorporating market trends and letting certain assumptions of existing models to relax in order to better fit into the current global scenario is the need of the hour. In this paper, an attempt is made to relax one of the assumptions of the Bass model which states that both the innovators and imitators contribute to the initial purchases of the product with the only difference of their buying influence. In a more realistic scenario, we consider that there exists a distinction in the two categories based on their timings of adoption. Though, imitators would adopt throughout the diffusion process but initial purchases of the product would be majorly through innovators. Then only the word-of-mouth effect would spread in masses which results in product adoption by imitators. Based on this assumption of time delay between the adoption of product by an innovator and then by an imitator, we propose time-delay effect based innovation diffusion models. Sometimes mutually dependent imitators would adopt a product if and only if the innovators have already adopted the product. Therefore, into the innovation diffusion modeling framework, we incorporate a concept of innovators dependent imitation process. New models are proposed and they are tested against real life data sets. Investigational results demonstrate precise forecasting ability for the proposed framework.