Acta Geographica Sinica ›› 2019, Vol. 74 ›› Issue (2): 203-221.doi: 10.11821/dlxb201902001

Special Issue: 人口与城市研究

• Population and Urban Studies •     Next Articles

Gravity model coefficient calibration and error estimation: Based on Chinese interprovincial population flow

ZHAO Ziyu1(),WEI Ye2(),YANG Ran2,WANG Shijun2,ZHU Yu3   

  1. 1. Department of Public Administration, Ningbo University, Ningbo 315211, Zhejiang, China
    2. School of Geographical Sciences, Northeast Normal University, Changchun 130024, China
    3. Institute of Geography, Fujian Normal University, Fuzhou 350007, China
  • Received:2017-07-12 Online:2019-02-25 Published:2019-01-29
  • Supported by:
    National Natural Science Foundation of China, No.41401172, No.41630749


Simulations based on spatial interaction models have been widely applied to understand the strength of relationships between geographical elements, but many issues remain unclear and deviations between actual and simulated results have often been seriously underestimated. A high-precision Baidu migration process combined with mass relationships is applied in this study and enables the generation of regression coefficients of gravity model based on programmed large-scale regression simulations. A series of accuracy assessments are then developed for 2015 empirical projection daily regression coefficients that can be applied to Chinese spring interprovincial mobile gravity model variables as well as spatiotemporal research that utilizes regression coefficients within a heterogeneity research model. This approach also enables the error within the gravity model to be assessed in terms of floating population simulations. The results of this analysis lead to a number of clear conclusions, including the fact that parameter calibration complexity for the Chinese population mobility gravity model is reflected in the degree of influence asymmetry within spatial object interaction variables, and that the spatial heterogeneity of the variable regression coefficient increases in two distinct fashions. The first of these increases has to do with the overall influence of specific variables, including the fact that differences between proxies tend to be higher than inflow-outflow characteristics. In contrast, the second set of increases is related to economic levels, industrial scales, the proportion of the tertiary industry, and public service facilities. In this latter case, two-way population flow exerts a more profound influence on results and thus the scope of possible explanations for phenomena is more extensive. The regression coefficient for the existence of positive and negative proxy variables therefore relates to differences in spatial heterogeneity, including at the city level, and also assumes that floating population gravity model regression coefficients ignore spatiotemporal changes in the heterogeneity coefficient. This leads to spatial differences in estimated results and thus convergence trends, but further enables the identification of anisotropic interactions in extension space. The second main conclusion of this research is that the national scale population flow distance attenuation coefficient was 1.970 during the spring of 2015, while at the level of prefectural administrative units and given population outflow, the range encapsulated by this coefficient fell between 0.712 (Zhumadian) and 7.699 (Urumqi). Data also reveal a population inflow coefficient of 0.792 for this year that ranged as high as 8.223 in both Sanya and Urumqi. Population flow simulation results using the gravity model and including Baidu migration measured flow data were also subject to significant error. Third, the results of this analysis reveal a total fitting error of 85.54% in weighted absolute mean; the spatial interaction effect within this is responsible for a maximum error of 86.09% in actual and simulated flows, while relative outflow force and attractiveness encompass 57.73% and 49.34% of model error, respectively. These results show that the spatial interaction effect remains most difficult to model in terms of current factors.

Key words: gravity model, regression coefficient, distance attenuation coefficient, error estimation, population flow, China