逐步回归的时空地理加权变量选取方法
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摘要
针对当前建立时空地理加权回归模型采用一般的变量选择方法不考虑时间和空间因素的问题,该文提出一种基于逐步回归的时空地理加权变量选取方法。通过引入Akaike信息法则为变量的取舍准则,基于逐步回归,利用陕甘宁地区影响人口分布的变量与人口分布关系进行实际性能的实验验证。实验结果表明:该方法优于传统逐步回归法、向前引入法和向后剔除法。
According to the problem that there are not consider the issue of time and space factors,when the phenomena are analysed by Geographically and Temporally Weight Regression,(GTWR).the paper,proposes a new method that the method of selecting GTWR variable based on stepwise regression.Based on the stepwise regression,the paper analysis the distribution and its influencing factors in the Shanxi-Gansu-Ningxia region by introducing Akaike's information rule as an example.The experimental results show that the method of selecting GTWR Based on Stepwise Regression is superior to the traditional stepwise regression,forward and backward method.The research results haves a new variable selection method for GTWR analysis.
According to the problem that there are not consider the issue of time and space factors,when the phenomena are analysed by Geographically and Temporally Weight Regression,(GTWR).the paper,proposes a new method that the method of selecting GTWR variable based on stepwise regression.Based on the stepwise regression,the paper analysis the distribution and its influencing factors in the Shanxi-Gansu-Ningxia region by introducing Akaike's information rule as an example.The experimental results show that the method of selecting GTWR Based on Stepwise Regression is superior to the traditional stepwise regression,forward and backward method.The research results haves a new variable selection method for GTWR analysis.
引文
[1]SONG W,JIA H,HUANG J,et al.A satellite-based geographically weighted regression model for regional PM2.5estimation over the Pearl River delta region in China[J].Remote Sensing of Environment,2014,154:1-7.
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[5]刘天,刘瑛,钟杰.PM2.5成因的逐步回归分析及治理方案研究[J].数学的实践与认识,2014,44(15):77-79.(LIU Tian,LIU Ying,ZHONG Jie.Stepwise analysis and control scheme research on PM2.5[J].Mathematics in Practics and Theory,2014,44(15):77-79.)
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[7]HUANG C,TOWNSHEND J R G.A stepwise regression tree for nonlinear approximation:applications to estimating subpixel land cover[J].International Journal of Remote Sensing,2003,24(1):75-90.
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[10]CLIFFORD M,HURVICH,JEFFREY S,et al.Smoothing parameter selection in nonparametric regression using an improved akaike information criterion[J].Journal of the Royal Statistical Society Series B-statistical Methodology,1998:271-293.
[11]BRUNSDON C,FOTHERINGHAM A S,CHARL-TON M.Geographically weighted summary statistics:a framework for localized exploratory data analysis[J].Computers,Environment and Urban Systems,2002,26(6):501-524.
[12]玄海燕,罗双华,王大斌.GWR模型中权函数的选取与窗宽参数的确定[J].甘肃联合大学学报(自然科学版),2008,22(3):10-12.(XUAN Haiyan,LUOShuanghua,WANG Dabin.Selecting weight function and determining bandwidth parameter of GWR model[J].Journal of Gansu Lianhe University(Natural Sciences),2008,22(3):10-12.)
[13]FOTHERINGHAM A S,BRUNSDON C,CHARL-TON M.Geographically weighted regression,the analysis of spatially varying relationships[M].New York:John Wiley&Sons,Let,2002:34-45.
[14]杨毅.顾及时空非平稳性的地理加权回归方法研究[D].武汉:武汉大学,2016:27-28.(YANG Yi.Research on geographically and temporally weighted regression for spatial and temporal nonstationarity[D].Wuhan:Wuhan University,2016:27-28.)
[15]王美红,康国栋.陕西县域经济发展与SO2排放及环境容量测评[J].环境与可持续发展,2011(1):28-32.(WANG Meihong,KANG Guodong.Economic development SO2 emission and environmental capacity assessment in Shaanxi[J].Environmen and Sustainable Development,2011(1):28-32.)
[16]孙根年.国家区域公路网密度与人口密度、人均GNP关系的统计分析[J].西南交通大学学报,2000,35(2):220-223.(SUN Gennian.Statistics analysis on the relationship of highway net density with population density and per capita GNP in national region[J].Journal of Southwest Jiaotong University,2000,35(2):220-223.)
[2]HUANG B,WU B.Geographically and temporally weighted regression for spatiotemporal modeling of house prices[J].International journal of Geographical Information Science,2010(3):383-401.
[3]赵阳阳,刘纪平,张福浩,等.贪心算法的地理加权回归特征变量选择方法[J].测绘科学,2016,41(7):42-45.(ZHAO Yangyang,LIU Jiping,ZHANG Fuhao,et al.An approach of characteristics variable selection based on greedy algorithm in geographically weighted regression[J].Science of Surveying and Mapping,2016,41(7):42-45.)
[4]张云海,孙财涛,杨洪斌.基于逐步回归分析方法的PM10浓度预报模型[J].环境科学与技术,2009,32(5):101-102.(ZHANG Yunhai,SUN Caitao,YANGHongbin.PM10concentration forecast model based on stepwise regression analysis[J].Environmental Science&Technology,2009,32(5):101-102.)
[5]刘天,刘瑛,钟杰.PM2.5成因的逐步回归分析及治理方案研究[J].数学的实践与认识,2014,44(15):77-79.(LIU Tian,LIU Ying,ZHONG Jie.Stepwise analysis and control scheme research on PM2.5[J].Mathematics in Practics and Theory,2014,44(15):77-79.)
[6]CHUN Y,GRIFFITH DA,LEE M,et al.Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters[J].Journal of Geographical Systems,2016,18:67-85.
[7]HUANG C,TOWNSHEND J R G.A stepwise regression tree for nonlinear approximation:applications to estimating subpixel land cover[J].International Journal of Remote Sensing,2003,24(1):75-90.
[8]LU B,CHARLTON M,HARRIS P,et al.Geographically weighted regression with a non-euclidean distance metric:a case study using hedonic house price data[J].International Journal of Geographical Information Science,2014,28(4):660-681.
[9]HURVICH C M,SIMONOFF J S,TSAI C,et al.Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion[J].Journal of the Royal Statistical Society Series B-statistical Methodology,1998,60(2):271-293.
[10]CLIFFORD M,HURVICH,JEFFREY S,et al.Smoothing parameter selection in nonparametric regression using an improved akaike information criterion[J].Journal of the Royal Statistical Society Series B-statistical Methodology,1998:271-293.
[11]BRUNSDON C,FOTHERINGHAM A S,CHARL-TON M.Geographically weighted summary statistics:a framework for localized exploratory data analysis[J].Computers,Environment and Urban Systems,2002,26(6):501-524.
[12]玄海燕,罗双华,王大斌.GWR模型中权函数的选取与窗宽参数的确定[J].甘肃联合大学学报(自然科学版),2008,22(3):10-12.(XUAN Haiyan,LUOShuanghua,WANG Dabin.Selecting weight function and determining bandwidth parameter of GWR model[J].Journal of Gansu Lianhe University(Natural Sciences),2008,22(3):10-12.)
[13]FOTHERINGHAM A S,BRUNSDON C,CHARL-TON M.Geographically weighted regression,the analysis of spatially varying relationships[M].New York:John Wiley&Sons,Let,2002:34-45.
[14]杨毅.顾及时空非平稳性的地理加权回归方法研究[D].武汉:武汉大学,2016:27-28.(YANG Yi.Research on geographically and temporally weighted regression for spatial and temporal nonstationarity[D].Wuhan:Wuhan University,2016:27-28.)
[15]王美红,康国栋.陕西县域经济发展与SO2排放及环境容量测评[J].环境与可持续发展,2011(1):28-32.(WANG Meihong,KANG Guodong.Economic development SO2 emission and environmental capacity assessment in Shaanxi[J].Environmen and Sustainable Development,2011(1):28-32.)
[16]孙根年.国家区域公路网密度与人口密度、人均GNP关系的统计分析[J].西南交通大学学报,2000,35(2):220-223.(SUN Gennian.Statistics analysis on the relationship of highway net density with population density and per capita GNP in national region[J].Journal of Southwest Jiaotong University,2000,35(2):220-223.)