Multiclass Compactness Index for Urban Areas

Often urban compactness indexes ignore the variegated intensity of urban development in their focus on the configuration. In this article, I propose an extension to the index of moment of inertia (IMI) as a compactness measure that can account for multiple ordinal classes representing development intensity. I demonstrate this index for developed areas for each county in the contiguous United States. These counties have a range of development configurations and intensity compositions. I show that for this data set, ignoring the multiple class composition and only focusing on the configuration overestimates the urban compactness in almost all instances. I demonstrate the impact of different analytical choices on the index for this data set.