The hidden side of the entropy-based land-use mix index: Clarifying the relationship between pedestrian volume and land-use mix

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.