地理探测器的空间分层模型选择理论

空间分异是自然和社会经济规律在地理空间上的客观存在，是自亚里士多德以来人类认识和探究自然规律的窗口。地理探测器是探测空间分异性，揭示其背后驱动因子的一套新的统计学方法。2010年提出了地理探测器模型和2016年推导出了其概率密度函数以来，目前已经被24个国家和地区的学者使用，运用于56个广泛学科，发表了800多篇学术论文，包括多篇国际顶刊。地理探测器可处理类型量，但对于数值量，需要空间分层(stratification)。目前的分层方法一般基于学科习惯、等间距、K-means和q最大等方式，尚缺少严格的空间统计学依据。本申请拟对已有的几百种分类模型和算法从各自的假设条件、机理和数据要求进行解析，研建一棵分类算法的“演化树”，作为地理探测器备选分层模型集合；建立不同分层方式q统计差的概率密度函数，支撑最优分层模型选择；借鉴AIC理论推导最优分层数目，以上三点形成地理探测器的分层模型选择理论。

Spatial stratified heterogeneity (SSH) origins from the laws of nature and socioeconomics and appears on geospace. It is also the window for human to recognize, describe and explore the nature laws since Aristotle (384-322BC) time. Geodetector is a novel statistic to measure and explore the driving forces of SSH. Since the publications of the estimator in 2010 and its probability density function (pdf) in 2016, scholars from 24 countries and regions have been applying Geodetector to publish more than 800 research articles in 56 scientific disciplines, some in Nature and Lancet series. Geodetector handles categorical variables; quantitative variables should be stratified, usually by customs in disciplines, equalized interval partition, K-means and the q maximum. Actually, there are hundreds of algorithms for classification, zonation and clustering, but there is no rule of thumb yet for choice of the methods of stratification. This proposal will anatomize the existing methods, then construct a tree like structure to link the methods according to the evolution and mutation of their principles. The evolution tree of the stratification methods will be ready for model choice; another job is to derive the pdf of the q difference between two stratifications; and the third is to derive a criterion for the optimal number of strata, referring to AIC theory. The three points constitute the stratification model choice theory for Geodetector.