Bass Model And Its Two Extensions Applied Research

The innovation diffusion models have been attracting the attention of people from the sixth decade of twenty century when the innovation diffusion theories were introduced into the fields of technology forecasting and market theory. There are sorts of innovation diffusion models in these fields, and the Bass model is the most famous one among them. The diffusion models have become the main domain of market theory when the Bass model was brought forward in 1969. The Bass model and it's extended models are used widely in the aspects of describing and forecasting for a innovation diffusion process. But the validity of Bass model is disbelieved for sometimes. In fact, the Bass model is valid just only for a few of products' diffusion curves, and people attempt to reduce the hypothesis of Bass model, and increase the applicability of the model, so many extended models based on Bass model are introduced, but none of them are used as widely as the Bass model. The innovation diffusion models are applied more and more widely and deeply in the market of American and Europe, but this study in China just begins, no matter the diffusion theories or the applications for Bass model are drop behind out and away comparing to the developed the countries.The paper aims at the application methods of Bass model and the two extended models that can embody the relation of products' diffusion. The technical route of this paper is that, at first, taking the Bass model for example, the researches of the structure, the application method and the validity of market diffusion for an innovation diffusion model are presented after reviewing and searching literature, and then, this paper analyzes the limitation of a dependent product' diffusion adopting Bass model, and constructs a contingent diffusion model for the products that show the characteristic of contingent relationship.In the research of the application methods of Bass model, the paper concludes that the choices for the data series and the estimate methods for the parameters of Bass model influence the effects of fitness and forecasting after studying the BP and mobile subscribers diffusion curves. The started point, the time interval of data and the number of data points is very important for the Bass model. This paper adopts OLS( ordinary least square), MLE (Maximum-likelihood estimation),NLS(Nonlinear Least Squares) and GA( Genetic Algorithms) respectively for estimating the parameters of Bass model, and GA gets the best fitness, furthermore, employing GA to estimate the parameters of Bassmodel can gain a better forecasting when there are just only five or six data points for Bass model, this is very significant for the forecasting of a product in the growth phase .In order to convince the results of Bass model ,the fitness of Bass model is compared with the other two S curves ,Logistic curve and Gompertz curve, and the Bass model is super among them.In the research of the extended models for Bass model, the paper points out the limitation of Bass model's hypothesis that the diffusion of a product is independent. It has been nearly 40 years from Bass model, there are fewer and fewer products to adapt to Bass model. Especially for high-technology products, the diffusion of products always contacts with each other. It can not build up an exact model for these products if Bass model is directly adopted without considering other product diffusion. So the paper focuses on the following two extended aspects about Bass model:The one is the research of the model for the adoption and substitution for successive generations of the modes of connecting Internet in China .The paper takes the Norton model to fit the three mode of connecting Internet, and gets some satisfied results. But the estimating parameters of Norton for this research are different from the Norton model hypothesis, the Norton model supposes that the innovation coefficient of each generation pi is equal to others(p= pO, and the imitation coefficient q; is the same situation (q= qO.so ,from the paper ,the author considers that each generation of the Norton has itself parameters, it is not truth for the hypothesis of the Norton p= pi, q= qj.The other is modeling for the contingent diffusion product based on Bass model after analyzing and defining the characteristic of a contingent product. This model is called "contingent diffusion model" in this paper, and this model is applied in the contingent diffusion of the service of wireless Internet based on the wireless subscribers, and then this paper compares the results of the contingent diffusion model with that of the Bass model, and the comparing shows that no matter the fitness or the forecasting, the contingent diffusion model is better than the Bass model for a contingent product diffusion.