Spatial effect on the diffusion of discount stores (대형할인점 확산에 대한 공간적 영향)
- Joo, Young-Jin;Kim, Mi-Ae
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- Journal of Distribution Research
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- v.15 no.4
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- pp.61-85
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- 2010
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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.Innovative Converged Service and It's Adoption, Use and Diffusion : A Holistic Approach to Diffusion of Innovations, Combining Adoption-Diffusion and Use Diffusion Paradigms (디지털융합서비스의 수용, 사용, 확산에 관한 연구 : 혁신확산에 관한 수용-확산 및 사용-확산의 통합적 접근)
- Sawng, Yeong-Wha;Rim, Myung-Hwan;Kim, Seong-Ho;Motohashi, Kazuyuki
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- Journal of Information Technology Applications and Management
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- v.17 no.2
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- pp.187-205
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- 2010
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This study takes a holistic approach to understand the diffusion of IPTV services by combining the adoption-diffusion model and the use-diffusion model of innovation. IPTV service, a leading digital converged application coupling media content with telecommunications, has been recently launched commercially in Korea. We created a structural model of adoption-diffusion, using the perceived easeof-use and usefulness of TAM(Technology Acceptance Model) as mediating variables, and a structural model of use-diffusion, with the rate of use and the variety of use as mediating variables. To empirically analyze these models, non-users of IPTV were surveyed using the adoption-diffusion model to identify factors influencing their intention to subscribe to the service. Meanwhile, users of IPTV were surveyed using the use-diffusion model to determine the factors that influence their satisfaction with the service and their intention to re-use it. Under the adoption-diffusion model, we found that trialability, household innovativeness and perceived risk were the determinants of user satisfaction with IPTV, and perceived ease-of-use, the mediating factors. Under the use-diffusion model, complementarity and communication were shown to be the determinants of users' satisfaction with IPTV, and variety of use, the mediating factor. We also found that consumers' intention to re-use IPTV was strongly influenced by its relative advantage and perceived risk.
Innovative Converged Service and It's Adoption, Use and Diffusion: A Holistic Approach to Diffusion of Innovations, Combining Adoption-Diffusion and Use Diffusion Paradigms (디지털융합서비스의 수용, 사용, 확산에 관한 연구: 혁신확산에 관한 수용-확산 및 사용-확산의 통합적 접근)
- Song, Yeong-Hwa;Im, Myeong-Hwan;Motohashi, Kazuyuki;Kim, Seung-Ho
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- Proceedings of the Korea Database Society Conference
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- 2010.06a
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- pp.165-180
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- 2010
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This study takes a holistic approach to understanding the diffusion of IPTV services by combining the adoption-diffusion model and the use-diffusion model of innovation. IPTV service, a leading Digital converged application coupling media content with telecom, has been recently launched commercially in Korea. We created a structural model of adoption-diffusion, using the perceived ease-of-use and usefulness of TAM(Technology Acceptance Model) as mediating variables, and a structural model of use-diffusion, with the rate of use and the variety of use as mediating variables. To empirically analyze these models, non-users of IPTV were surveyed using the adoption-diffusion model to identity factors influencing their intention to subscribe to the service. Meanwhile, users of IPTV were surveyed using the use-diffusion model to determine the factors that influence their satisfaction with the service and their intention to fe-use it. Under the adoption-diffusion model, we found that trialability, household innovativeness and perceived risk were the determinants of user satisfaction with IPTV, and perceived ease-of-use, the mediating factors. Under the use-diffusion model, complementarity and communication were shown to be the determinants of users' satisfaction with IPTV, and variety of use, the mediating factor. We also found that consumers' intention to re-use IPTV was strongly influenced by its relative advantage and perceived risk.
ERROR ESTIMATES FOR OPTION PRICES IN JUMP-DIFFUSION MODELS
- Wee, In-Suk
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- Bulletin of the Korean Mathematical Society
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- v.39 no.4
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- pp.705-714
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- 2002
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We consider a jump-diffusion model generated by a Levy process for an asset price. We present an error estimate for the option prices between the jump-diffusion model and the Black-scholes model when the former converges weakly to the latter.
Pile tip grouting diffusion height prediction considering unloading effect based on cavity reverse expansion model
- Jiaqi Zhang;Chunfeng Zhao;Cheng Zhao;Yue Wu;Xin Gong
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- Geomechanics and Engineering
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- v.37 no.2
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- pp.97-107
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- 2024
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The accurate prediction of grouting upward diffusion height is crucial for estimating the bearing capacity of tip-grouted piles. Borehole construction during the installation of bored piles induces soil unloading, resulting in both radial stress loss in the surrounding soil and an impact on grouting fluid diffusion. In this study, a modified model is developed for predicting grout diffusion height. This model incorporates the classical rheological equation of power-law cement grout and the cavity reverse expansion model to account for different degrees of unloading. A series of single-pile tip grouting and static load tests are conducted with varying initial grouting pressures. The test results demonstrate a significant effect of vertical grout diffusion on improving pile lateral friction resistance and bearing capacity. Increasing the grouting pressure leads to an increase in the vertical height of the grout. A comparison between the predicted values using the proposed model and the actual measured results reveals a model error ranging from -12.3% to 8.0%. Parametric analysis shows that grout diffusion height increases with an increase in the degree of unloading, with a more pronounced effect observed at higher grouting pressures. Two case studies are presented to verify the applicability of the proposed model. Field measurements of grout diffusion height correspond to unloading ratios of 0.68 and 0.71, respectively, as predicted by the model. Neglecting the unloading effect would result in a conservative estimate.
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
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- IE interfaces
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- v.23 no.4
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- pp.337-348
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- 2010
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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.
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
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- 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
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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 Comparison Study of the Prediction Performance of FDS Combustion Model for the Jet Diffusion Flame Structure (제트 확산화염구조에 대한 FDS 연소모델의 예측성능 비교 연구)
- Park, Eun-Jung;Oh, Chang-Bo
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- Journal of the Korean Society of Safety
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- v.25 no.3
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- pp.22-27
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- 2010
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A prediction performance of Fire Dynamics Simulator(FDS) developed by NIST for the diffusion flame structure was validated with experimental results of a laminar slot jet diffusion flame. Two mixture fraction combustion models and two finite chemistry combustion models were used in the FDS simulation for the validation of the jet diffusion flame structure. In order to enhance the prediction performance of flame structure, DNS and radiation model was applied to the simulation. The reaction rates of the finite chemistry combustion models were appropriately adjusted to the diffusion flame. The mixture fraction combustion model predicted the diffusion flame structure reasonably. A 1-step finite chemistry combustion model cannot predict the flame structure well, but the simulation results of a 2-step model were in good agreement with those of experiment except
$CO_2$ concentration. It was identified that the 2-step model can be used in the investigation of flame suppression limit with further adjustment of reaction rates
Development of the intermittency turbulence model for a plane jet flow (자유 평면 제트유동 해석을 위한 간혈도 난류모델의 개발)
- 조지룡;정명균
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- Transactions of the Korean Society of Mechanical Engineers
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- v.11 no.3
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- pp.528-536
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- 1987
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In a turbulent free shear flow, the large scale motion is characterized by the intermittent flow which arises from the interaction between the turbulent fluid and the irrotational fluid of the environment through the mean velocity gradient. This large scale motion causes a bulk convection whose effect is similar to the spatial diffusion process. In this paper, the total diffusion process is proposed to be approximated by weighted sum of the bulk convection due to the large scale motion and the usual gradient diffusion due to small scale motion. The diffusion term in conventional .kappa.-.epsilon. model requires on more equation of the intermittency transport equation. A production term of this equation means mass entrainment from the irrotational fluid to the turbulent one. In order to test the validity of the proposed model, a plane jet is predicted by this method. Numerical results of this model is found to yield better agreement with experiment than the standard .kappa.-.epsilon. model and Byggstoyl & Kollmann's model(1986). Present hybrid diffusion model requires further tests for the check of universality of model and for the model constant fix.
Asymmetric Diffusion Model for Protein Spot Matching in 2-DE Image (2차원 전기영동 영상의 단백질 반점 정합을 위한 비대칭 확산 모형)
- Choi, Kwan-Deok;Yoon, Young-Woo
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- The KIPS Transactions:PartB
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- v.15B no.6
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- pp.561-574
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- 2008
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The spot detection phase of the 2-DE image analysis program segments a gel image into spot regions by an image segmentation algorithm and fits the spot regions to a spot shape model and quantifies the spot informations for the next phases. Currently the watershed algorithm is generally used as the segmentation algorithm and there are the Gaussian model and the diffusion model for the shape model. The diffusion model is closer to real spot shapes than the Gaussian model however spots have very various shapes and especially an asymmetric formation in x-coordinate and y-coordinate. The reason for asymmetric formation of spots is known that a protein could not be diffused completely because the 2-DE could not be processed under the ideal environment usually. Accordingly we propose an asymmetric diffusion model in this paper. The asymmetric diffusion model assumes that a protein spot is diffused from a disc at initial time of diffusing process, but is diffused asymmetrically for x-axis and y-axis respectively as time goes on. In experiments we processed spot matching for 19 gel images by using three models respectively and evaluated averages of SNR for comparing three models. As averages of SNR we got 14.22dB for the Gaussian model, 20.72dB for the diffusion model and 22.85dB for the asymmetric diffusion model. By experimental results we could confirm the asymmetric diffusion model is more efficient and more adequate for spot matching than the Gaussian model and the diffusion model.
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