• Title/Summary/Keyword: 공간확산모형

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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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