Implementing a multilevel index of dissimilarity in R with a case study of the changing scales of residential ethnic segregation in England and Wales

This paper introduces the MLID package, which provides tools and functions to fit a Multilevel Index of Dissimilarity in the open source software, R. It extends the conventional Index of Dissimilarity (ID) to measure both the amount and geographic scale of segregation, thereby capturing the two principal dimensions of segregation, unevenness and clustering. The statistical basis for the multilevel approach is discussed, making connections to other work in the field and looking especially at the relationships between the ID, variance as a measure of segregation, and the partitioning of the variance to identify scale effects. A brief tutorial for the package is provided followed by a case study of the scales of residential segregation for various ethnic groups in England and Wales. Comparing 2001 with 2011 Census data, we find that patterns of segregation are emerging at less localised geographical scales but the ID is falling. This is consistent with a process whereby minority groups have spread out into more ethnically mixed neighbourhoods.