Editing Principal component analysis (section)

=== Residential differentiation ===
In 1949, Shevky and Williams introduced the theory of '''factorial ecology''', which dominated studies of residential differentiation from the 1950s to the 1970s.<ref>{{Cite book |last1=Shevky |first1=Eshref |title=The Social Areas of Los Angeles: Analysis and Typology |last2=Williams |first2=Marilyn |publisher=University of California Press |year=1949}}</ref> Neighbourhoods in a city were recognizable or could be distinguished from one another by various characteristics which could be reduced to three by factor analysis. These were known as 'social rank' (an index of occupational status), 'familism' or family size, and 'ethnicity'; Cluster analysis could then be applied to divide the city into clusters or precincts according to values of the three key factor variables. An extensive literature developed around factorial ecology in urban geography, but the approach went out of fashion after 1980 as being methodologically primitive and having little place in postmodern geographical paradigms.

One of the problems with factor analysis has always been finding convincing names for the various artificial factors. In 2000, Flood revived the factorial ecology approach to show that principal components analysis actually gave meaningful answers directly, without resorting to factor rotation. The principal components were actually dual variables or shadow prices of 'forces' pushing people together or apart in cities. The first component was 'accessibility', the classic trade-off between demand for travel and demand for space, around which classical urban economics is based. The next two components were 'disadvantage', which keeps people of similar status in separate neighbourhoods (mediated by planning), and ethnicity, where people of similar ethnic backgrounds try to co-locate.<ref>Flood, J (2000). Sydney divided: factorial ecology revisited. Paper to the APA Conference 2000, Melbourne, November and to the 24th ANZRSAI Conference, Hobart, December 2000.[https://www.academia.edu/5135339/Sydney_Divided_Factorial_Ecology_Revisited]</ref>

About the same time, the Australian Bureau of Statistics defined distinct indexes of advantage and disadvantage taking the first principal component of sets of key variables that were thought to be important. These SEIFA indexes are regularly published for various jurisdictions, and are used frequently in spatial analysis.<ref>{{Cite web |last= |first= |date=2011 |title=Socio-Economic Indexes for Areas |url=https://www.abs.gov.au/websitedbs/censushome.nsf/home/seifa |access-date=2022-05-05 |website=Australian Bureau of Statistics |language=en}}</ref>