title: Disentangling collective trends from local dynamics.
abstract: A single social phenomenon (such as crime, unemployment, or birthrate) can be observed through temporal series corresponding to units at different levels (i.e., cities, regions, and countries). Units at a given local level may follow a collective trend imposed by external conditions, but also may display fluctuations of purely local origin. The local behavior is usually computed as the difference between the local data and a global average (e.g, a national average), a viewpoint that can be very misleading. We propose here a method for separating the local dynamics from the global trend in a collection of correlated time series. We take an independent component analysis approach in which we do not assume a small average local contribution in contrast with previously proposed methods. We first test our method on synthetic series generated by correlated random walkers. We then consider crime rate series (in the United States and France) and the evolution of obesity rate in the United States, which are two important examples of societal measures. For the crime rates in the United States, we observe large fluctuations in the transition period of mid-70s during which crime rates increased significantly, whereas since the 80s, the state crime rates are governed by external factors and the importance of local specificities being decreasing. In the case of obesity, our method shows that external factors dominate the evolution of obesity since 2000, and that different states can have different dynamical behavior even if their obesity prevalence is similar.
authors.affiliation: Institut de Physique Théorique, Commissariat à l'Energie Atomique, URA 2306 Centre National de la Recherche Scientifique F11191 Gif-sur-Yvette, France. marc.barthelemy@cea.fr
authors.forename: Marc
authors.initials: M
authors.lastname: Barthélemy
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Nadal
authors.forename: Henri
authors.initials: H
authors.lastname: Berestycki
mesh_terms: D003627:Data Interpretation, Statistical; D005602:France; D006801:Humans; D008962:Models, Theoretical; D009765:Obesity / Q000453:epidemiology*; D012919:Social Behavior; D012940:Social Problems / Q000706:statistics & numerical data*; D013997:Time Factors; D014481:United States / Q000453:epidemiology
references.citation: Phys Rev Lett. 2004 Aug 6;93(6):068701
references.pmid: 15323670
references.citation: JAMA. 2004 Jun 16;291(23):2847-50
references.pmid: 15199035
references.citation: JAMA. 2006 Apr 5;295(13):1549-55
references.pmid: 16595758
references.citation: Obes Res. 2001 Nov;9 Suppl 4:228S-233S
references.pmid: 11707546
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Feb;49(2):1685-9
references.pmid: 9961383
references.citation: Epidemiol Rev. 2007;29:6-28
references.pmid: 17510091
references.citation: JAMA. 1999 Oct 27;282(16):1519-22
references.pmid: 10546690
references.citation: Phys Rev Lett. 2004 Jan 16;92(2):028701
references.pmid: 14753972