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Comparison of the Bass Model and the Logistic Model from the Point of the Diffusion Theory

확산이론 관점에서 로지스틱 모형과 Bass 모형의 비교

  • 홍정식 (서울과학기술대학교 IT정책전문대학원 산업정보시스템전공) ;
  • 구훈영 (충남대학교 경상대학 경영학부)
  • Received : 2011.08.25
  • Accepted : 2012.05.23
  • Published : 2012.06.30

Abstract

The logistic model and the Bass model have diverse names and formulae in diffusion theory. This diversity makes users or readers confused while it also contributes to the flexibility of modeling. The method of handling the integration constant, which is generated in process of deriving the closed form solution of the differential equation for a diffusion model, results in two different 'actual' models. We rename the actual four models and propose the usage of the models with respect to the purpose of model applications. The application purpose would be the explanation of historical diffusion pattern or the forecasting of future demand. Empirical validation with 86 historical diffusion data shows that misuse of the models can draw improper conclusions for the explanation of historical diffusion pattern.

Keywords

Acknowledgement

Supported by : 서울과학기술대학교

References

  1. 홍정식, 김태구, 임달오, "확산 모형에 의한 고가의료기기의 수요 확산의 특성분석 및 중장기 수요예측에 관한 연구", 보건행정학회지, 제18권, 제4호(2008), pp.85-110.
  2. 홍정식, 엄석준, "Bass 확산 모형의 이분 확장", 한국경영과학회지, 제34권, 제4호(2009), pp. 15-26.
  3. Bemmaor, A.C. and J. Lee, "The Impact of Heterogeneity and Ill-Conditioning on Diffusion Model Parameter Estimates," Marketing Science, Vol.21, No.2(2002), pp.209-220. https://doi.org/10.1287/mksc.21.2.209.151
  4. Hu, Q., C. Saunders and M. Gebelt, "Research Report;Diffusion of Information Systems Outsourcing; A Reevaluation of Influence Sources," Information Systems Research, Vol.8, No.3(1997), pp.288-301. https://doi.org/10.1287/isre.8.3.288
  5. Kingsland, S., "The Refractory Model;The Logistic Curve and the History of Population Ecology," The Quarterly Review of Biology, Vol.57, No.1(1982), pp.29-52. https://doi.org/10.1111/j.1469-185X.1982.tb00363.x
  6. Li, Y. and Z. Chen, "Diffusion of Innovations in a Small World Network," Wireless Communications, Networking and Mobile Computing, (2007), pp.5617-5620.
  7. Meade, N., "Forecasting Using Growth Curves- An Adaptive Approach," The Journal of the Operational Research Society, Vol.36, No.12 (1985), pp.1103-1115.
  8. Meade, N. and T. Islam, "Forecasting with growth curves;An empirical comparison," International Journal of Forecasting, Vol.11, No.2(1995), pp.199-215. https://doi.org/10.1016/0169-2070(94)00556-R
  9. Meade, N. and T. Islam, "Technological Forecasting- Model Selection, Model Stability, and Combining Models," Management Science, Vol.44, No.8(1998), pp.1115-1130. https://doi.org/10.1287/mnsc.44.8.1115
  10. Meyer, P.S., J.W. Yung, and J.H. Ausubel, "A primer on logistic growth and substitution; The mathematics of the loglet lab software," Technological Forecasting and Social Change, Vol.61(1999), pp.247-71. https://doi.org/10.1016/S0040-1625(99)00021-9
  11. Muller, E. and G. Yogev, "When does the majority become a majority? Empirical analysis of the time at which main market adopters purchase the bulk of our sales," Technological Forecasting and Social Change, Vol.73(2006), pp.1107-1120. https://doi.org/10.1016/j.techfore.2005.12.009
  12. Niu, S., "A Piecewise-Diff-usion Model of New-Product Demands," Operations Research, Vol.54, No.4(2006), pp.678-695. https://doi.org/10.1287/opre.1060.0287
  13. Ozkaya, E., Demand management in global supply chains, Ph. D. Thesis, Georgia Institute of Technology, 2008.
  14. Philips, F., "On S-curves and tipping points," Technological Forecasting and Social Change, Vol.74(2007), pp.715-730. https://doi.org/10.1016/j.techfore.2006.11.006
  15. Reed, L.J. and R. Pearl, "On the summation of logistic curves," Journal of the Royal Statistical Society, Vol.90, No.4(1927), pp. 729-746. https://doi.org/10.2307/2341367
  16. Satoh, D., "A discrete bass model and its parameter estimations," Journal of the Operations Research Society of Japan, Vol.44, No.1 (2001), pp.1-18.
  17. Van den Bulte, C. and Y.V. Joshi, "New Product Diffusion with Influentials and Imitators," Marketing Science, Vol.26, No.3(2007), pp. 400-21. https://doi.org/10.1287/mksc.1060.0224
  18. Verhulst, P.F., "Recherches mathematiques sur la loi d'accroissement de la population," Mem. Acad. Roy. Belg., Vol.18(1845), pp.1-38.
  19. Wang, H. and H. Doong, "Diffusion of mobile music service in Taiwan;an empirical investigation of influence sources," Management Decision, Vol.48, No.9(2010), pp.1378- 1387. https://doi.org/10.1108/00251741011082125
  20. Wu, F. and W. Chu, "Diffusion models of mobile telephony," Journal of Business Research, Vol.63, No.5(2010), pp.497-501. https://doi.org/10.1016/j.jbusres.2009.04.008

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