Exploring the Variability of Segregation Index D with Scale and Zonal Systems: An Analysis of Thirty US Cities

In this paper, we propose a methodology to study the scale effect and zoning effect of the modifiable areal unit problem (MAUP). Instead of aggregating basic spatial units by the neighborhood criterion, we suggest placing a square lattice over the centroids representing the enumeration units in the study area. Areal units are aggregated if their centroids are in the same square. By changing the size of the square in the lattice, we can study the scale effect. By randomly placing the lattice, we can study the zoning effect. This methodology links the MAUP effects to specific scale reflected by the size of grids. We use this method to study the MAUP effects on the segregation index D. Among the thirty selected cities in the USA, values of D respond to the MAUP in a diverse pattern. We assess the scale effect on D by examining the changes of averaged values of D over the range of scale levels. We also borrow concepts from fractal analysis to assess the scale effect on D and to measure how sensitive the D values of these cities are to different zonal patterns.