地理科学 ›› 2002, Vol. 22 ›› Issue (5): 581-586.doi: 10.13249/j.cnki.sgs.2002.05.581

• 论文 • 上一篇    下一篇

效用最大化、logit变换和城市地理学的数量分析模型

陈彦光1, 刘继生2, 房艳刚2   

  1. 1. 北京大学城市与环境学系 北京 100871;
    2. 东北师范大学地理系 吉林 长春 130024
  • 收稿日期:2002-03-10 修回日期:2002-04-27 出版日期:2002-09-20 发布日期:2002-09-20
  • 基金资助:
    国家自然科学基金资助项目的部分内容(项目编号:40071035)。

Utility-Maximization, Logit Transformation and the Basic Mathematical Models for Analytical Urban Geography

CHEN Yan-guang1, LIU Ji-sheng2, FANG Yan-gang2   

  1. 1. Department of Geography, Peking University, Beijing 100871;
    2. Department of Geography, Northeast Normal University, Changchun, Jilin 130024
  • Received:2002-03-10 Revised:2002-04-27 Online:2002-09-20 Published:2002-09-20

摘要: 城市地理学的主要数学模型,包括城市化进程的logistic模型,城市位序-规模分布的幂指数模型以及城市人口密度衰减的负指数模型,都可以从两个简单的科学假设出发推导出来。文章证明,上述假设在理论上可以归结为效用最大化原理,其本质与信息熵最大化有着深刻的内在关系。城市地理学的主要模型作为标度定律都可以借助logit变换进行简化处理,从而为理论模型的实际应用以及城市演化动力学的模拟实验分析打开了方便之门。

Abstract: Many basic mathematical models as scale laws can be derived from a pair of assumptions, i.e. ① The utility in some sense is proportional to some kinds of variables such as time, space, and class; ② The respondent variables of the utility such as population size and city number is the exponential function of the utility. The basic models include the allometric relationship of urban and rural population, logistical model of urbanization process, the relationship between level of urbanization and that of economic development, i.e. Zhou’s model, urban population density model, i.e. Clark’s model, the generalized Beckmann-Davis model, and the three-parameter Zipf model, etc. It is proved that the exponential relationships between the utility and its respondency come from utility-maximization that is consistent with entropy-maximization, and utility-maximization and entropy-maximization are actually principles of duality. Ont the other hand, the basic models for analytical urban geography can be changed into logit models, for example, the urban and rural population allometric model is linked to binary logit model (BLM), and the Clark model can be connected with multinomial logit model (MNL). This means that we can simulate the urban dynamics based on utility-maximization principle by means of logit transformation that can simplify the researched objects to a great extent. The logit transformation will become an important part of geocomputation and the simulation based on the logit models consociated with utility-maximization principle will contribute to the studies of spatial complexity. Utility-maximization is not only one of the general principles of urban geography but the foundation of urban maximization from which we can develop new methods for urban planning. Perhaps the consistence of utility-maximization and entropy-maximization is the key to solving the problems of spatial complexity. Unlike the concepts such as "the edge of chaos" and "self-organized criticality", the duality of utility-and entropy-maximization can answer many theoretical questions without using one concept to replace another.

中图分类号: 

  • P290