Comparing measures of urban land use mix

•Reviews mathematical formulas and conceptual underpinnings for a wide range of measures of urban land use mix.•Conducts a Monte Carlo simulation to discover statistical relationships between various mixed use measures.•Compares results from the Monte Carlo simulation to empirical data from Hillsboro, Oregon.•Identifies crucial limitations of mixed use measures and discusses techniques for adapting to those limitations.•Provides recommendations about which mixed use measure to use based upon available contextual information.

We review a variety of common measures of urban land use mix in order to understand their differences and to identify their strengths and limitations. We then apply these measures to data from a Monte Carlo simulation to ascertain statistical relationships among them, finding that they can be placed into four groups where measures within each group produce highly consistent results: Percentage and Exposure Index; all varieties of the Atkinson Index; Balance, Entropy, and Herfindahl–Hirschman indices; and the Dissimilarity and Gini indices. We find that when analyzing two dimensions of land use, generally both the Balance Index and the Dissimilarity Index should be used, and that the Dissimilarity Index should be tested at multiple scales. We provide a number of other practical recommendations about which mixed use measure to apply given the contextual information available to a researcher or analyst.

Graphical abstract(A) Modifiable areal unit problem: The scores of divisional measures can be sensitive to the specific geography of divisions. With the same land use distribution but different district sizes, Dissimilarity = 1.00 for the 3 × 3 grid on the left, but Dissimilarity = 0.8125 for the 4 × 4 grid on the right. (B) Insensitivity to area-wide land use concentration. Dissimilarity Index produces the same value (Dissimilarity = 1) as does Gini Index (Gini = 1) despite very different levels of land use concentration at the areal level. On the other hand, integral measures will vary between these two areas. (C) Permutation of districts: These two area’s districts have the same land use distributions, but different spatial arrangements. Most divisional measures (except the Clustering Index) will produce the same score for both areas.Figure optionsDownload full-size imageDownload as PowerPoint slide