基于个体移动轨迹的多中心城市引力模型验证

长期以来由于规模变量、距离衰减系数取值缺乏依据,引力模型在城市研究中的应用容易受到质疑,加之中国城市的多中心化使得模型应用的外部条件发生改变,模型验证工作的必要性再次显现。本文使用2015年移动通信用户的个体移动轨迹数据,使用Huff当年的验证方法,通过变量检验、参数校正两个步骤,验证Huff的引力模型。研究发现：① 城市内部商业中心和就业中心的吸引力与中心的规模呈正比,与距中心的距离呈反比,符合引力模型规律。② 在上海中心城区空间尺度、200 m网格空间单元下,商业中心吸引力的距离衰减系数平均值为2.5,就业中心吸引力的距离衰减系数平均值为3.0,表明居民就业通勤对距离更加敏感,距离衰减比购物出行更加显著。③ 经变量检验、参数校正后的引力模型可用于对商业中心、就业中心优化调整后的势力范围进行预测,预测准确率可分别达到78.5%和71.9%。就业中心势力范围预测准确性略低,这是由于就业中心吸引力衰减除受距离影响外,还受家庭、房价等因素影响,会对预测结果产生扰动。最后,研究还证实了距离衰减系数存在空间分层异质性：距离衰减系数不是唯一值,受道路可达性、至就业（商业）中心距离、至地铁站距离、人口密度影响,不同地区的距离衰减系数存在较显著差异。

Validating gravity model in multi-centre city: A study based on individual mobile trajectory

Due to the lack of empirical studies of scale variables and distance exponents, the effective application of the gravity model in urban study is challenging. With the development of multi-centralized Chinese cities, the gravity model must be validated because several relevant external conditions have changed. The purpose of this study is to validate Huff's Gravity Model using an individual mobile trajectory of mobile communication user in 2015. We follow Huff's two-step validation method: variable validation and parameter correction. Our main conclusions are as follows. First, attractions of commercial and employment centres conform to the law of the gravity model in which the attraction is proportional to the scale of a centre and inversely proportional to the distance from a centre. Second, in the spatial scale of Shanghai central city with spatial units in a 200-m grid, the mean distance exponent for commercial centres is 2.5 and that for employment centres is 3.0. The distance decay for commuting is greater than that for shopping trips, which means commuting is more sensitive to distance. Third, the gravity model can be used to predict the influence areas of adjusted commercial and employment centres based on validated variables and corrected parameters. Our results indicate that the prediction accuracies can reach 78.5% and 71.9% for the commercial and employment centres, respectively. The prediction accuracy for employment centres is slightly lower. This is because the attraction of employment centres is influenced not only by distance but also by factors such as family and housing prices, which will affect the prediction results. Lastly, in this study, we verify the spatial stratified heterogeneity of distance decay and determine that the distance exponent is not a unique constant because it has different values in different areas. Factors such as accessibility, distance to each centre, distance to a subway station and population density will affect distance decay.