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

Abstract

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.

Measuring pedestrian volume by land use mix: Presenting a new entropy-based index by weighting walking generation units

“…3 Korea Transport Surveys and DB Construction Projects (Korea Transport Institute, 2001) show that different pedestrian volumes are generated through various building use categories: residential is 0.11 person/m 2 /day, commercial is 0.85/m 2 /day, office is 0.35/m 2 /day, and other is 0.33/m 2 /day. Applying these values for CLUM2 in residential and non-residential uses, one can draw a straight line, which is similar to the one that can be drawn for estimated pedestrian volume in Figure 1 (Im and Choi, 2019). This straight line serves as a logical image of the pedestrian volume created when mixing residential and nonresidential uses, and it reconfirms a limitation of CLUM.…”

“…Some analyses using the index have not presented statistically positive effects of LUM on pedestrian volume and, in certain cases, have even shown a negative relationship. Im and Choi (2019) found that the LUM index had a critical limitation beyond those already discussed by Kockelman (1996), Brown et al (2009), Hess et al (2001), and others. They confirmed that the conventional entropy-based land use mix index (hereafter, CLUM) has an n-shaped relationship with pedestrian volume and that, in the case of the sample from the whole city, the explanatory power of pedestrian volume increased in the empirical model when using both CLUM and CLUM squared rather than only using CLUM.…”

“…Most previous studies analysing the characteristics of CLUM have not discussed the fundamental characteristics of the index. However, Im and Choi (2019) showed the nonlinear characteristic of CLUM. An example of this is shown in Figure 1, in which point 'a' comprises a mixture of 80% residential and 20% commercial use and point 'b' comprises 80% commercial and 20% residential use, with both equal to 0.72 of the CLUM value.…”

“…This issue is even more evident when CLUM2 is plotted in linear form in Figure 1. The CLUM2 value is the dotted line and the quadratic function curve: the form of the 'n' shape for CLUM2 makes a fixed relationship with the dependent variable difficult (Im and Choi, 2019). On the left side of the vertex in Figure 1, CLUM2 and the estimated pedestrian volume have a positive (þ) relationship, but on the right side, they have a negative (À) relationship.…”

“…This straight line serves as a logical image of the pedestrian volume created when mixing residential and nonresidential uses, and it reconfirms a limitation of CLUM. Im and Choi (2019) show how using CLUM4 and CLUM4 2 together in the empirical estimation model for pedestrian volume is logical. CLUM generates a positive pedestrian volume (þ) coefficient, and CLUM4 2 generates a negative (À) one.…”