The Index of Relative Rurality (IRR) is a continuous, threshold-free, and unit-free measure of rurality. The original version of the IRR was proposed by Waldorf (2006, http://ageconsearch.umn.edu/handle/21383) as an alternative to the traditional discrete threshold-based classifications, such as the Rural-urban Continuum Code and the Urban Influence Code. Waldorf and Kim (2015) designed an improved county level IRR for 2000 and 2010. The IRR has three major advantages over typology-based rurality measures. (1) It is spatially flexible in that it can be designed for any spatial units; (2) it is a relative measure and thus embeds rurality in the broader system of settlements; (3) it is analytically more easily handled than threshold-based typologies. The IRR ranges between 0 (low level of rurality, i.e., urban) and 1 (most rural). Four steps are involved in its design: Identifying the dimensions of rurality: population size, density, remoteness, and built-up area. Selecting measureable variables to adequately represent each dimension: Size: logarithm of population size Density: logarithm of population density. Remoteness: network distance. Built-up area: urban area (as defined by the US Census Bureau) as a percentage of total land area. Re-scaling the variables onto bounded scales that range from 0 to 1. Selecting a link function: unweighted average of the four re-scaled variable. For more information: Waldorf, Brigitte, and Ayoung Kim. 2015. "Defining and Measuring Rurality in the US: From Typologies to Continuous Indices." Commissioned paper prepared for the National Academies of Sciences Workshop on Rationalizing Rural Classifications, April 2015, Washington, DC http://sites.nationalacademies.org/cs/groups/dbassesite/documents/webpage/dbasse_168031.pdf
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Waldorf et al. (2018) studied this question.