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 effectand zoning effect of the modifiable areal unit problem (MAUP). Insteadof aggregating basic spatial units by the neighborhood criterion, we suggestplacing a square lattice over the centroids representing the enumerationunits in the study area. Areal units are aggregated if their centroidsare 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 canstudy the zoning effect. This methodology links the MAUP effects to specificscale reflected by the size of grids. We use this method to study theMAUP effects on the segregation index D . Amongthe 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 valuesof D over the range of scale levels. We also borrowconcepts 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.