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.

This study proposes an alternative to the conventional entropy-based land use mix index, which is generally used to measure the diversity of land use. Pedestrian volume was selected as the dependent variable as it represents the vitality of districts, which many recent urban studies now consider important. The study investigates an entropy-based weighted land use mix index, which is weighted by different land use types. For the index, different areas are needed to generate a unit of pedestrian volume, whose measure is m2/person/day. The study demonstrates that this alternative is more effective than the existing conventionally used entropy-based land use mix index for explaining pedestrian volume. The research confirms that the conventionally used entropy-based land use mix index can have a positive or negative impact depending on the land use characteristics of the survey points because the conventionally used entropy-based land use mix index has a non-linear relationship with pedestrian volume. By analysing 9727 surveyed locations of pedestrian volume in Seoul, Korea, the study demonstrates that the weighted land use mix index, rather than the conventionally used entropy-based land use mix index, can improve the explanatory power of the estimation model for the relationship between pedestrian volume and built environments, showing consistent results throughout the empirical analysis. In future built-environment studies, the utility of the weighted land use mix index is expected to improve if studies include how to find the accurate weighting of the land use in estimating the pedestrian volume.

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