将集体趋势与地方动态分开
Disentangling collective trends from local dynamics
摘要：
一个单一的社会现象（如犯罪、失业或出生率）可以通过对应于不同级别（城市、区域、国家.）单位的时间序列来观察。某一地方一级的单位可能遵循外部条件所造成的集体趋势，但也可能显示纯粹源于地方的波动。当地行为通常被计算为当地数据和全球平均值（例如全国平均值）之间的差异，这是一种非常误导的观点。我们在这里提出了一种方法，用于分离当地的动态从全球趋势的相关时间序列的集合。我们采取一个独立的成分分析方法，在该方法中，我们不假设一个小的无偏的本地贡献与以前提出的方法相比。我们首先测试我们的方法相关的随机游走生成的合成系列。然后，我们考虑犯罪率系列（在美国和法国）和肥胖率在美国的演变，这是社会措施的两个重要例子。就犯罪率而言，全球政策和地方政策的分离是一个主要的辩论主题。就美国而言，我们观察到70年代中期的转型期出现了大幅波动，在此期间犯罪率大幅上升，而自80年代以来，各州的犯罪率受外部因素的影响，地方特殊性的重要性正在下降。在肥胖症的情况下，我们的方法表明，外部因素主导了自2000年以来的肥胖症的演变，不同的国家可以有不同的动力学行为，即使他们的肥胖患病率是相似的。
英文摘要：
A single social phenomenon (such as crime, unemployment or birth rate) can be observed through temporal series corresponding to units at different levels (cities, regions, 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 view point which 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 unbiased 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 US and France) and the evolution of obesity rate in the US, which are two important examples of societal measures. For crime rates, the separation between global and local policies is a major subject of debate. For the US, we observe large fluctuations in the transition period of mid-70's during which crime rates increased significantly, whereas since the 80's, 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.
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