商圈惠顾行为的空间衰减：幂律模式还是指数模式

以上海市商业中心为例，基于匿名手机信令数据，运用引力模型对商圈惠顾行为的衰减模式及其系数进行了验证与对比。结果表明，① 对于商圈惠顾行为，最常用的2种距离衰减函数均具有较高的拟合优度，幂律函数稍优于指数函数；② 总体来看，距离仍是影响城市居民商圈惠顾行为的关键因素，距离衰减效应呈现出随商业中心等级增大而减弱的梯度特征，幂律型衰减系数取值1~3不等，采用既定系数1或2会过高/低估计商圈辐射能力；③ 不可忽视闲暇时间对商圈惠顾行为的约束作用，与周末相比，工作日的距离衰减系数较大，且商业中心等级越低，商圈惠顾行为的衰减性越显著。

The Spatial Decay of Patronizing Behavior in Trade Areas:Power Law or Exponential Law

The spatial decay of retail patronizing behavior in trade areas exists objectively, but there is a controversy about the power law and exponential law and no conclusion on the distance-decay mode has been reached to date. Exploring spatial decay modes and parameters will help to optimize urban commercial space structure and provide scientific advices. Taking examples of 14 commercial centers in Shanghai, this study aims to analyze and validate the distance-decay law and its coefficients of retail travel behavior, based on mobile phone signaling data in 2013. We compare and examine the distance decay modes and coefficients of varying scale commercial centers in different leisure time. The results show that both power and exponential distance-decay modes have high goodness of fits, the adjusted R² is greater than 0.6 for most of commercial centers. In comparison, power law function fits better slightly, but the advantage is not significant, the goodness of fit of the former is only slightly higher about 0.05 than the later. Meanwhile, the distance is still a key factor affecting retail travel behavior of urban residents, and distance-decay coefficient decreases with the size of commercial centers increasing, especially on weekday. Power-law distance decay coefficient is between 1 and 2 for commercial centers, which has strong spatiotemporal heterogeneity. Such as, the distance decay coefficient of Zhenru commercial center is up to 2.084, while that of East Nanjing road commercial center is 1.010. So the radiation capacity of commercial centers will be too overestimate or underestimate if given coefficient 1 or 2 is adopted. Another conclusion of this research is that the constraint effect of leisure time on retail travel behavior cannot be ignored. Compared with weekend, the distance decay parameter on weekday is larger, and the smaller the commercial center size is, the more significant the distance decay is. The coefficient differences between weekend and weekday for East Nanjing road and Xujiahui commercial centers are smaller, which is less than 0.3. While there are significant differences in varying leisure time for Zhenru and Zhonghuan commercial centers.