• Title/Summary/Keyword: Bass Diffusion Model

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Forecasting the Growth of Smartphone Market in Mongolia Using Bass Diffusion Model (Bass Diffusion 모델을 활용한 스마트폰 시장의 성장 규모 예측: 몽골 사례)

  • Anar Bataa;KwangSup Shin
    • The Journal of Bigdata
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    • v.7 no.1
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    • pp.193-212
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    • 2022
  • The Bass Diffusion Model is one of the most successful models in marketing research, and management science in general. Since its publication in 1969, it has guided marketing research on diffusion. This paper illustrates the usage of the Bass diffusion model, using mobile cellular subscription diffusion as a context. We fit the bass diffusion model to three large developed markets, South Korea, Japan, and China, and the emerging markets of Vietnam, Thailand, Kazakhstan, and Mongolia. We estimate the parameters of the bass diffusion model using the nonlinear least square method. The diffusion of mobile cellular subscriptions does follow an S-curve in every case. After acquiring m, p, and q parameters we use k-Means Cluster Analysis for grouping countries into three groups. By clustering countries, we suggest that diffusion rates and patterns are similar, where countries with emerging markets can follow in the footsteps of countries with developed markets. The purpose was to predict the timing and the magnitude of the market maturity and to determine whether the data follow the typical diffusion curve of innovations from the Bass model.

Two Pieces Extension of the Bass Diffusion Model (Bass 확산모형의 이분 확장)

  • Hong, Jung-Sik;Eom, Seok-Jun
    • Journal of the Korean Operations Research and Management Science Society
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    • v.34 no.4
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    • pp.15-26
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    • 2009
  • Bass diffusion model have played a central role in studying the diffusion of the new products since 1969, the year of publication of Bass model. Almost 750 publications based on the Bass diffusion model have explored extensions and applications. Extension models can be divided into two types. One is the model containing marketing-mix variables and the other is the model containing additional parameters. This paper presents another extension model of the latter type. Our model allows the time varying coefficients of innovation and imitation. Two pieces approximation of time varying coefficients is introduced and it's parameters are estimated based on NLS(Non-Linear Mean Square) method. Empirical studies are performed and the results show that our model is superior to the basic Bass model and the NUI(Non-Uniform Influence) model which is the well-known extension of the Bass model. The model developed in this paper is, also, transformed into the Bass model with the ready potential adopters in order to enhance the descriptive power.

Spatial effect on the diffusion of discount stores (대형할인점 확산에 대한 공간적 영향)

  • Joo, Young-Jin;Kim, Mi-Ae
    • Journal of Distribution Research
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    • v.15 no.4
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    • pp.61-85
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    • 2010
  • Introduction: Diffusion is process by which an innovation is communicated through certain channel overtime among the members of a social system(Rogers 1983). Bass(1969) suggested the Bass model describing diffusion process. The Bass model assumes potential adopters of innovation are influenced by mass-media and word-of-mouth from communication with previous adopters. Various expansions of the Bass model have been conducted. Some of them proposed a third factor affecting diffusion. Others proposed multinational diffusion model and it stressed interactive effect on diffusion among several countries. We add a spatial factor in the Bass model as a third communication factor. Because of situation where we can not control the interaction between markets, we need to consider that diffusion within certain market can be influenced by diffusion in contiguous market. The process that certain type of retail extends is a result that particular market can be described by the retail life cycle. Diffusion of retail has pattern following three phases of spatial diffusion: adoption of innovation happens in near the diffusion center first, spreads to the vicinity of the diffusing center and then adoption of innovation is completed in peripheral areas in saturation stage. So we expect spatial effect to be important to describe diffusion of domestic discount store. We define a spatial diffusion model using multinational diffusion model and apply it to the diffusion of discount store. Modeling: In this paper, we define a spatial diffusion model and apply it to the diffusion of discount store. To define a spatial diffusion model, we expand learning model(Kumar and Krishnan 2002) and separate diffusion process in diffusion center(market A) from diffusion process in the vicinity of the diffusing center(market B). The proposed spatial diffusion model is shown in equation (1a) and (1b). Equation (1a) is the diffusion process in diffusion center and equation (1b) is one in the vicinity of the diffusing center. $$\array{{S_{i,t}=(p_i+q_i{\frac{Y_{i,t-1}}{m_i}})(m_i-Y_{i,t-1})\;i{\in}\{1,{\cdots},I\}\;(1a)}\\{S_{j,t}=(p_j+q_j{\frac{Y_{j,t-1}}{m_i}}+{\sum\limits_{i=1}^I}{\gamma}_{ij}{\frac{Y_{i,t-1}}{m_i}})(m_j-Y_{j,t-1})\;i{\in}\{1,{\cdots},I\},\;j{\in}\{I+1,{\cdots},I+J\}\;(1b)}}$$ We rise two research questions. (1) The proposed spatial diffusion model is more effective than the Bass model to describe the diffusion of discount stores. (2) The more similar retail environment of diffusing center with that of the vicinity of the contiguous market is, the larger spatial effect of diffusing center on diffusion of the vicinity of the contiguous market is. To examine above two questions, we adopt the Bass model to estimate diffusion of discount store first. Next spatial diffusion model where spatial factor is added to the Bass model is used to estimate it. Finally by comparing Bass model with spatial diffusion model, we try to find out which model describes diffusion of discount store better. In addition, we investigate the relationship between similarity of retail environment(conceptual distance) and spatial factor impact with correlation analysis. Result and Implication: We suggest spatial diffusion model to describe diffusion of discount stores. To examine the proposed spatial diffusion model, 347 domestic discount stores are used and we divide nation into 5 districts, Seoul-Gyeongin(SG), Busan-Gyeongnam(BG), Daegu-Gyeongbuk(DG), Gwan- gju-Jeonla(GJ), Daejeon-Chungcheong(DC), and the result is shown

    . In a result of the Bass model(I), the estimates of innovation coefficient(p) and imitation coefficient(q) are 0.017 and 0.323 respectively. While the estimate of market potential is 384. A result of the Bass model(II) for each district shows the estimates of innovation coefficient(p) in SG is 0.019 and the lowest among 5 areas. This is because SG is the diffusion center. The estimates of imitation coefficient(q) in BG is 0.353 and the highest. The imitation coefficient in the vicinity of the diffusing center such as BG is higher than that in the diffusing center because much information flows through various paths more as diffusion is progressing. A result of the Bass model(II) shows the estimates of innovation coefficient(p) in SG is 0.019 and the lowest among 5 areas. This is because SG is the diffusion center. The estimates of imitation coefficient(q) in BG is 0.353 and the highest. The imitation coefficient in the vicinity of the diffusing center such as BG is higher than that in the diffusing center because much information flows through various paths more as diffusion is progressing. In a result of spatial diffusion model(IV), we can notice the changes between coefficients of the bass model and those of the spatial diffusion model. Except for GJ, the estimates of innovation and imitation coefficients in Model IV are lower than those in Model II. The changes of innovation and imitation coefficients are reflected to spatial coefficient(${\gamma}$). From spatial coefficient(${\gamma}$) we can infer that when the diffusion in the vicinity of the diffusing center occurs, the diffusion is influenced by one in the diffusing center. The difference between the Bass model(II) and the spatial diffusion model(IV) is statistically significant with the ${\chi}^2$-distributed likelihood ratio statistic is 16.598(p=0.0023). Which implies that the spatial diffusion model is more effective than the Bass model to describe diffusion of discount stores. So the research question (1) is supported. In addition, we found that there are statistically significant relationship between similarity of retail environment and spatial effect by using correlation analysis. So the research question (2) is also supported.

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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)

    • Hong, Jung-Sik;Koo, Hoon-Young
      • Journal of the Korean Operations Research and Management Science Society
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      • v.37 no.2
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      • pp.113-125
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      • 2012
    • 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.

    A Study on Forecast of Penetration Amount of High-Efficiency Appliance Using Diffusion Models (확산 모형을 이용한 고효율기기의 보급량 예측에 관한 연구)

    • Park, Jong-Jin;So, Chol-Ho;Kim, Jin-O
      • Journal of Energy Engineering
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      • v.17 no.1
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      • pp.31-37
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      • 2008
    • At present, the target amount of demand-side management and investment cost of EE (Energy Efficiency) program, which consists of high-efficiency appliances, has been estimated simply by the diffusion function based on the real historical data in the past or last year. In the internal and external condition, the penetration amount of each appliance has been estimated by Bass diffusion model which is expressed by time and three coefficients. And enough acquisition of real historical data is necessary for reasonable estimation of coefficients. In energy efficiency, to estimate the target amount of demand-side management, the penetration amount of each appliance should be primarily forecasted by Bass diffusion model in Korea. On going programs, however, lightings, inverters, vending machine and motors have a insufficient real historical data which is a essential condition to forecast the penetration amount using a Bass diffusion model due to the short period of program progress. In other words, the forecast of penetration amount may not be exact, so that it is necessary for the method of forecast to apply improvement of method. In this paper, the penetration amount of high-efficiency appliances is forecasted by Bass, virtual Bass, Logistic and Lawrence & Lawton diffusion models to analyze the diffusion progress. And also, by statistic standards, each penetration is compared with historical data for model suitability by characteristic of each appliance. Based on the these result, in the forecast of penetration amount by diffusion model, the reason for error occurrence caused by simple application of diffusion model and preferences of each diffusion model far a characteristic of data are analyzed.

    A Modified Diffusion Model Considering Autocorrelated Disturbances: Applications on CT Scanners and FPD TVs (자기상관 오차항을 고려한 수정된 확산모형: CT-스캐너와 FPD TV에의 응용)

    • Cha, Kyoung Cheon;Kim, Sang-Hoon
      • Asia Marketing Journal
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      • v.11 no.1
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      • pp.29-38
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      • 2009
    • Estimating the Bass diffusion model often creates a time-interval bias, which leads the OLS approach to overestimate sales at early stages and underestimate sales after the peak. Further, a specification error from omitted variables might raise serial correlations among residuals when marketing actions are not incorporated into the diffusion model. Autocorrelated disturbances may yield unbiased but inefficient estimation, and therefore invalid inference results. This phenomenon warrants a modified approach to estimating the Bass diffusion model. In this paper, the authors propose a modified Bass diffusion model handling autocorrelated disturbances. To validate the new approach, authors applied the method on two different data-sets: CT Scanners in the U.S, and FPD TV sales in Korea. The results showed improved model fit and the validity of the proposed model.

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    Analysis of Diffusion Pattern in New Product and Services Based on Two-pieces Bass Model (신제품 및 서비스에 있어 이분조각 Bass모형에 의한 확산 패턴 분석)

    • Hong, Seok-Kee;Hong, Jung-Sik
      • IE interfaces
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      • v.23 no.4
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      • pp.337-348
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      • 2010
    • The Bass model is the most widely used model in research of new product diffusion because it presents a nice explanation on the diffusion process of new products. However, it has a limitation that its performance of fitness is lower as the available data become less and also, the diffusion curve is bell-shape and so, it can not represent the various diffusion patterns. Recently, a two-pieces Bass model is developed and applied to analyze diffusion of 10 products. The results are encouraging in terms of fitness. However, diffusion pattern is not dealt with in the paper. In this paper, analysis of diffusion pattern is in depth addressed in two-pieces Bass model. It is shown that the diffusion curves are divided into 3 types with respect to the peak adoption rate and each type is divided into 2 types further. Takeoff time of a diffusion process is analyzed by using the inflection point and regime-change time where it represents the point that imitation and innovation parameters change. Empirical studies for 68 products(28 domestic products and 40 USA products) are performed to analyze the diffusion pattern. Findings are that diffusion patterns of all products except 1 USA product show type I and regime-change time becomes shorter as the introduction time of the product is later in domestic products and regime-change time can be regarded as a takeoff time in 47% of total 68 products.

    Forecasting the Diffusion of Innovative Products Using the Bass Model at the Takeoff Stage: A Review of Literature from Subsistence Markets

    • Mitra, Suddhachit
      • Asian Journal of Innovation and Policy
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      • v.8 no.1
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      • pp.141-161
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      • 2019
    • A considerable amount of research has been directed at subsistence markets in the recent past with the belief that these markets can be tapped profitably by marketers. Consequently, such markets have seen the launch of a number of innovative products. However, marketers of such forecasts need timely and accurate forecasts regarding the diffusion of their products. The Bass model has been widely used in marketing management to forecast diffusion of innovative products. Given the idiosyncrasies of subsistence markets, such forecasting requires an understanding of effective estimation techniques of the Bass model and their use in subsistence markets. This article reviews the literature to achieve this objective and find out gaps in research. A finding is that there is a lack of timely estimates of Bass model parameters for marketers to act on. Consequently, this article sets a research agenda that calls for timely forecasts at the takeoff stage using appropriate estimation techniques for the Bass model in the context of subsistence markets.

    An Empirical Study of Technology Diffusion on the Internet using Bass Model (Bass 모형을 이용한 인터넷에서의 기술 확산에 대한 실증분석)

    • Nam, Ho-Hun;Yang, Kwang-Min
      • Journal of Digital Convergence
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      • v.6 no.2
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      • pp.55-64
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      • 2008
    • The Internet possesses not only features of mass media but also features of word of mouth communication. Communication channel is considered as one of most important variables in diffusion process. In this paper, we examined functionality of technology diffusion on the Internet through the use of meta tags. We have measured the coefficients of the Bass diffusion model which has been well-established in new product diffusion. This research shows that the Bass model is appropriate for describing technology diffusion on the Internet. The external influence as represented by the coefficient of innovation was found to be much smaller while the internal influence dominates in all meta tag diffusion. In meta tag diffusion, the internal influence as represented by the coefficient of imitation was increased at least twice bigger than that of consumer durables and information technology. Collecting necessary data in social sciences research can be a burden. This research shows that it can be alleviated through the use of software agents over the Internet. The research made use of software agents for collecting longitudinal data from publicly accessible archive such as Archive.org.

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    Network Based Diffusion Model (네트워크 기반 확산모형)

    • Joo, Young-Jin
      • Korean Management Science Review
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      • v.32 no.3
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      • pp.29-36
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      • 2015
    • In this research, we analyze the sensitivity of the network density to the estimates for the Bass model parameters with both theoretical model and a simulation. Bass model describes the process that the non-adopters in the market potential adopt a new product or an innovation by the innovation effect and imitation effect. The imitation effect shows the word of mouth effect from the previous adopters to non-adopters. But it does not divide the underlying network structure from the strength of the influence over the network. With a network based Bass model, we found that the estimate for the imitation coefficient is highly sensitive to the network density and it is decreasing while the network density is decreasing. This finding implies that the interpersonal influence can be under-looked when the network density is low. It also implies that both of the network density and the interpersonal influence are important to facilitate the diffusion of an innovation.


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