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This study clarifies the previously unknown limitations of the entropy-based land-use mix index and suggests conditions under which the index is valid. The land-use mix index has an n-shaped relationship to dependent variables, which was evidenced by this study, but previous studies have ignored the problem. This study identified a non-linear relationship between the land-use mix index and a common dependent variable of interest, pedestrian volume. Pedestrian volume is a common measure of the vitality of a district and/or a city and a major goal of urban design and regeneration. Using mathematical analysis, simulation, and empirical analysis, this study found that the land-use mix index had an inconsistent quadratic relationship to pedestrian volume. It was confirmed that an analytical model using the land-use mix index, and that index squared, should be used together when samples representative of entire cities are tested. Otherwise, in samples from predominantly residential areas, the land-use mix index positively relates to pedestrian volume, whereas, in predominantly commercial areas, it will be negative. Previous studies failed to observe the hidden side of the entropy-based land-use mix index in commercial areas because their focus was mainly on residential areas or residents. Future studies should clarify the logical and theoretical relationships between the index and the outcome variable of interest, review the characteristics of the data and, then, implement appropriate statistical analyses by being aware of the hidden side.
本研究阐明了以前未知的基于熵的土地利用综合指数的局限性，并提出了该指数有效的条件。土地利用综合指数与因变量呈 n 型关系，本研究证明了这一点，但以前的研究忽略了这个问题。本研究确定了土地利用综合指数与一个常用的因变量——行人流量——之间的非线性关系。行人流量是衡量区域和/或城市活力的常用指标，也是城市设计和再生的主要目标。利用数学分析、模拟和实证分析，本研究发现土地利用综合指数与行人流量之间有着不一致的二次方关系。我们已经证实，在对代表整个城市的样本进行测试时，土地利用综合指数分析模型和平方指数应一起使用。否则，在居住区占主导的样本中，土地利用综合指数与行人流量正相关，而在商业区主导的样本中则为负相关。先前的研究未能观察到商业区基于熵的土地利用综合指数的隐藏面，因为它们的重点主要集中在居住区或居民。未来的研究应该阐明该指数与相关结果变量之间的逻辑和理论关系，评估数据的特征，然后在明确意识到隐藏面的前提下实施合适的统计分析。