Aggregate diffusion forecasting models in marketing: A critical review

Parker, Philip M.

doi:10.1016/0169-2070(94)90013-2

Cited by 128 publications

(80 citation statements)

References 138 publications

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“…In an earlier but little-noted study, Martino (1972) had already shown that the bias in the least squares estimate of the slope parameter of a logistic diffusion model is proportional to the error in the estimate of the upper limit, but with the opposite sign. Many studies fitting Bass, Gompertz, and logistic diffusion models show results in which the estimates of ceiling and slope parameters are strongly negatively correlated (Bretschneider and Mahajan 1980, Debecker and Modis 1994, Jain and Rao 1990, Jones and Ritz 1991, Meade 1984, Oliver 1981, Parker 1993, Tigert and Farivar 1981.…”

Section: Introductionmentioning

confidence: 99%

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Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

1997

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Studies estimating the Bass model and other macra-leveldiffusion models with an unknown ceiling feature three curious empirical regularities: (i) the estimated ceiling is often close to the cumulative number of adopters in the last observation period, (ii) the estimated coefficient of social contagion or imitation tends to decrease as one adds later observations to the data set, and (iii) the estimated coefficient of social contagion or imitation tends to decrease systematically as the estimated ceiling increases.We analyze these patterns in detail, focusing on the Bass model and the nonlinear least squares (NLS) estimation method. Using both empirical and simulated diffusion data, we show that NLS estimates of the Bass model coefficients are biased and that they change systematically as oneextends the number of observations used in the estimation. We also idenhfy the lack of richness in the data compared to thecomplexity of the model (known as ill-conditioning) as the cause of these estimation problems.In an empirical analysis of twelve innovations, we assess how the model parameter estimates change as one adds later observations to the data set. Our analysis shows that, on average, a 10% increase in the observed cumulative market penetration is associated with, roughly, a 5% increase in estimated market size m, a 10% decrease in the estimated coefficient of imitation q, and a 15% increase the estimated coefficient of innovation p.A simulation study shows that the NLS parameter estimates of the Bass model change systematically as one adds later observations to the data set, even in the absence of model misspecification. We find about the same effect sizes as in the empirical analysis. The simulation also shows that the estimates are biased and that the amount of bias is a function of (i) the amount of noise in the data, (ii) the number of data points, and (iii) the difference between the cumulative penetration in the last observation period and the true penetration ceiling (i.e., the extent of right censoring). All three conditions affect the level of ill-conditioning in the estimation, which, in turn, affects bias in NLS regression. In situations consistent with marketing applications, m can be underestimated by 20% p underestimated by the same amount, and q overestimated by 30%.The existence of a downward bias in the estimate of m and an upward bias in the estimate of q, and the fact that these biases become smaller as the number of data points increases and the censoring decreases, can explain why systematic changes in the parameter estimates are observed in many applications. A reduced bias, though, is not the only possible explanation for the systematic change in parameter estimates observed in empirical studies. Not accounting for the growth in the population, for the effect of economic and marketing variables, or for population heterogeneity is likely to result in increasing m and decreasing $ as well. In an analysis of six innovations, however, we find that attempts to address possible model mis...

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Section: Introductionmentioning

confidence: 99%

“…Originally, researchers used ordinary least squares (OLS) to estimate model parameters, but more recently they have favored nonlinear least squares (NLS). The three-parameter, macro-level approach using NLS estimation has gained widespread acceptance (Mahajan et al 1993, Parker 1994.…”

Section: Introductionmentioning

confidence: 99%

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

1997

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“…Since its introduction, many researchers have proposed extensions to the original form of this model (Mahajan et al 1990;, Parker 1994). In addition, a summary of the applications of the extensions of the Bass model to telecoms can be found in Fildes and Kumar (2002).…”

Section: New Product Diffusionmentioning

confidence: 99%

Understanding the drivers of broadband adoption: the case of rural and remote Scotland

Howick

Whalley

2008

Journal of the Operational Research Society

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Broadband has been described as a transforming technology and is now widely available in many developed countries. However, broadband availability is not the same as broadband adoption. If the socio-economic benefits of broadband are to be realised, then adoption needs to be both understood and encouraged. This is particularly important in rural and remote areas. This paper explores the factors that drive broadband adoption in one particular rural and remote area; rural and remote Scotland. A causal model and a quantitative simulation model are developed indicating how the various drivers of adoption interact with one another. Both models show that past policy initiatives have impacted on the rate of adoption. However, the greatest impact could be achieved if future policy initiatives target those people who show no interest in adopting broadband. The paper concludes by suggesting that this work has implications for rural and remote areas all around the world.

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“…The research in literatures on modeling of the new product or innovation diffusion offered a lot of frameworks for the study of diffusion of information, ideas, and products. The details of those diffusion models in this area are available in many articles (Mahajan and Muller, 1979;Sultan et al, 1990;Mahajan et al, 1990;Parker, 1994;Hauser et al, 2006;Meade and Islam, 2006).…”

Section: Introductionmentioning

confidence: 99%

Research on Communication Products Diffusion in China Using Cellular Automata

Ma¹,

Gang-ling²

2011

IBR

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Based on cellular automata (CA), the diffusion of communication products, namely the mobile phone (MP) and the landline telephone (LT), were modeled and simulated. The ordinary least squares (OLS) procedure and nonlinear regression method were carried out to estimate the diffusion parameters. The predicted results were compared with the actual data. It is found that: (1) the diffusion processes of mobile phone and landline telephone were successfully examined using cellular automata method, (2) the predicted results of mobile phone and landline telephone show four stages of the product life cycle, (3) the present situation of mobile phones in China is at the fast growth stage and the present situation of landline telephone is at the maturity stage, (4) the market of mobile communication is growing fast and has a brighter future and the landline communication market is meeting great challenges. The future competition will be more serious between the mobile communication and the landline communication. Both of them can benefit from introduction of advanced technology and new services because such a strategy has the potential to convert some consumers of one of communications into another communications. As for the whole communications, the innovation of technology and services will be generated and introduced into the industry of communications to drive the market.

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Aggregate diffusion forecasting models in marketing: A critical review

Cited by 128 publications

References 138 publications

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models

Understanding the drivers of broadband adoption: the case of rural and remote Scotland

Research on Communication Products Diffusion in China Using Cellular Automata

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