Diffusion is a popular theory of communication used in marketing to model the first-purchase sales growth of a new product over time. As Mahajan et al (1990) put it diffusion theory suggests that a new product is first adapted by a few innovators who, in turn, influence others to adopt it. Taking this perspective on diffusion we can clearly see the pivotal role which interpersonal communication (word of mouth) between adopters and nonadopters plays in accounting for the rapid growth stage found in the diffusion process. It is important to remember that the value of diffusion modeling is not just restricted to historical data; rather leading academics in this field like Bass have made predictions based on early sales data which have resulted in successful predictions of diffusions before those products reached their peak. From a commercial perspective there are endless examples of diffusion processes, which will be elaborated on later, including: the diffusion of blockbuster movies; mobile phones and other analogous products. For the purposes of this assessment we will discuss the principal theories in this field playing particular attention to Bass and its variants, we will then apply these theories to the practical example of VCR diffusion.
[...] For the two other diffusion models considered in the study, (the Mansfield model and the Gompertz curve) the NLS again performs best and generally displays better predictions among the estimation procedures 6.1 Ordinary Least Squares Estimation (OLS) From Mahajan et al (1990), Bass uses a discrete analogue of his formula (as outlined above) and considers the case when the time intervals are equal to yearly data. Then, the probability that an initial purchase will be made in the ith time interval given that no purchase has yet been made, is expressed as a linear function of the number of previous adapters: = p+q/m N(ti-1) Advantages of OLS: Easy to implement Applicable to many different diffusion models Disadvantages of OLS: one may obtain parameter estimates that are unstable or possess wrong signs Standard Errors for the estimates are not available since the parameters m are nonlinear functions of α1, α2, α3 A time interval bias is present in OLS approach since discrete time- series data are used for estimating a continuous-time model Nonlinear least squares estimation (nls) This estimation procedure is designed to overcome the shortcomings of the maximum likelihood approach. [...]
[...] A number of estimation procedures have been suggested to estimate these parameters in the Bass model. From a practical standpoint it will be desirable to use subjective managerial judgment and/or experience with analogous products to estimate parameters prior to the launch of a new product. However for the purposes of this paper we will ignore the role of subjective judgment and concentrate on objective estimation procedures that require the availability of a reasonable amount of data (usually including the inflection point) to produce reliable estimates of model parameters. [...]
[...] Major assumptions: Price interacts with diffusion (rate of adoption ~ p value) Demand and saturation causes a decline in price over time Experience effect ( learning by doing) causes a decline in price over time Normative results: For a long planning period, if the imitation effect value) is dominating, price will at first increase and then decrease Source: Table 5 ~ optimal marketing mix strategies for innovation diffusion 19) of Mahajan et al (1990) 9.0 A look at the model using the VCR data set 9.1 Output & results BASS DIFFUSION MODEL.xls BASS MODEL NLS Time to peak sales, level of peak sales & point of inflection p (Coefficient of 0.008641089 Innovation) q (Coefficient of 0.635461538 Imitation) m (Market Potential) 68310.7368 (Point of Inflection) 0.493200935 (Time to Peak Sales) 6.672574788 (Level of Peak Sales) 11149.35772 Confidence intervals for the model parameters Asymptotic Asymptotic Confidence Interval Parameter Estimate Std. [...]
[...] we will discuss the principal theories in this field playing particular attention to Bass and its variants, we will then apply these theories to the practical example of VCR diffusion An Overview of the Bass Model The Bass model is one of most popular methods of modeling the first- purchase sales growth of a new product over time. It is most appropriate for forecasting the sales of an innovation for which no alternatives exist in the marketplace. From a practical standpoint we can see the critical importance of the Bass model for managers of such innovations forecasts can help managers come to a decision as to whether to invest significant resources in the project or not. [...]
[...] As a result, if we consider only successful innovations as analogs for our product, then the model will predict strong market forecasts for any new product, therefore adding to the potential for bias We can estimate the Bass model well from data only after making several observations of actual sales: But of course by the time we have collected this sales data the firm has already made critical investment decisions Technical Description of the Components of the Bass model The bass model can be written as: = Where: N = cumulative number of adopters at time t p = the coefficient of innovation q = the coefficient of imitation. [...]
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