動態空間交互模型的理論與實證分析

Abstract

本研究主要理論上推衍以最大熵概念為基礎的動態空間交互模型，並以電腦模擬探討此模型之特性。分析結果顯示以最大熵目標所推導的最適靜態區位流量估計式為基礎的區位選擇機率估計式恰符合數學logit模型的型式。由此靜態的區位選擇機率式所推導的動態機率估計式為基礎的動態空間交互模型有許多重要的特性：(一)此動態模型所解釋的成長過程對於參數值非常敏感。不同的參數值可導致完全不同結構的衍化過程。模擬結果顯示，同一動態模型可產生穩定與振動兩種不同的區域成長過程。同時在穩定的成長型式裡，參數與起始條件的不同會導致`不隨機`與`隨機`兩種不同的衍生結果。(二)此動態空間交互模型可模擬都市成長現象中最明顯卻又缺乏理論說明的法則：「Zipf`s Law」。模擬結果發現衍化時間越長，都市分佈越趨近於大小不均(與實證結果相近)，同時區位間利益的差異越大，衍化速度越快。區域中城市分佈的結構會收斂的因素主要是來自於變動的區位利益(聚集經濟)。

The purpose of this paper is to theoretically derive a dynamic spatial interaction model based on the entropy theory and use this derived growth process to explain the mysterious Zipf`s law. Empirical findings show that (1) the purposed dynamic process possibly generates both stable and unstable patterns according to the value of the parameters. (2) In the stable evolution, the model possibly generates both deterministic and stochastic growth processes. (3) Both deterministic and stochastic growth processes could converge to Zipf`s pattern. (4) Evidence from cities in Taiwan shows the diminishing estimated intercept and slope as the proposed model predicted. Size distribution in Taiwan converges to Zipf`s pattern.