城乡发展联系与空间统计建模分析
介绍内容
? 经济学原理
? 空间统计学原理
? 城乡发展联系的理论与建模分析
? 相关研究方向
Understanding the Economic Spatial Systems
应用地理学
?新经济
-Knowledge
-Information
-Globalization
?新科技
-Internet
-GIS&RS
-Spatial analytical tools
?新方法
-ESDA
-Spatial stats and
models
-Simulation
经济学
经济地理学
空间统计学
GIS&RS
Ｉ．经济学原理－新经济地理学
关于空间经济理论 -空间聚集的外部经济效应
目标 - 研究地区,城市和国际经济中下列因素相互作用,
? 增长回报效率
? 运输成本
? 生产要素的流动 (人力,物力,资本 )
空间聚集效应 -空间联系要素的作用与影响
? 知识扩散
? 市场经济中专门化技能的优势
? 与规模较大的地区市场相关的到流和正向联系
交通成本
距离（至城市中心）
蔬菜
麦
牲口
Von Thunen 模型, 土地租金与土地利用
土地租金 (愿付价格 )
效用函数,
最小化 {d} f (生产成本 + 交通成本 )
人口
纺织城市 金融城市
城市规模和产业结构
效用
II,空间统计学原理
? 环境研究中空间地理位置等因素日益增长的的重要性
? 空间 -时间变化比较
? 景观变化
? 空间分析技术发展 (GIS,RS & GPS)
? 对更高级和复杂分析方法的要求
关于空间统计学及应用的研究动因
? Why spatial data is different from non-spatial
data? (spatial neighborhood)
? Statistical property for spatial data,
? Spatial dependence (autocorrelation)
? Heterogeneity
? Spatial trend (non-stationarity)
? Sensitive to spatial boundaries and spatial unit
(Country,County,Tract) Elevation,Major cities and Lat /
Long grid
Why Spatial is Special?
空间分析问题
? Is there any spatial cluster over space?
? Are spatial observations distributed randomly over
space?
? Are spatial observations correlated (autocorrelation)?
? Is there any spatial outlier?
? Is there any spatial trend?
? What is the interaction (statistically and theoretically)
between different variables?
? How to predict an unknown spatial value at a specific
location,
常规统计学与空间统计学的差异
常规统计学 空间统计学
? Data,Time-series data Spatial data (cross-sectional)
? Relationship,Time (yt-1,yt,yt+1) Topology (yi-1,yi,yi+1)
? Process,{Z(t),t?T} {Z(s;t),s?D(t),t?T}
? Model,Y = ?WY + ?
t = 1,2,3,… wi,j = 1 if i is adjacent to j
? - time-series ? - spatial autocorrelation
autocorrelation
ttt YY ?? ?? ? 1
?空间抽样
?探索性数据分析
? 空间非稳定性检验
?空间自相关与联系检验
? 模型模拟与预测
? 数据驱动分析 (探索性数据分析 )
? 全程统计量
? 局部统计量
? 模型驱动分析
?空间线性模型
? 时空模型
空间统计学研究课题
?地理统计数据,
试验与理论方差图
协方差图和相关方差图
一般和通用插值法
空间过程拟合
?点数据,
空间随机检验
Ripley‘s K- 函数
局部聚集强度
空间随机过程模拟合
?网格数据,
全程空间自回归系数
局部空间相关系数
空间回归模型
网格数据拟合
空间统计数据分析功能
?空间稳定性与非稳定性检验 (variogram,covariogram,
correlogram,boxplots,trend model,and statistic graphics)
Experimental Variogram,
?空间自相关检验 (Moran I,Geary C,joint counts,Largrange Multiplier,
and Likelihood Ratio Test)
Moran I,
?空间关联检验 (G statistics,and LISA)
Local Moran,G Statistics,
Local Geary,
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空间分布模式分析
? 定义准则, 理论与经验方法
?可达性 (roads,rivers,railways,airlines and Internet)
?经济联系 (commuter flows,migrations,trade flows)
?社会联系 (college admission,language)
?地理位置联系 (neighborhood,geographical distance)
?定义方法,
?二进制距阵
?行标准化距阵
?权重函数 (wij=f(x,y..))
1 2
3
4
R O W, I D C O L, I D W E I G H T A W E I G H T B
1 2 1 0, 5
1 3 1 0, 5
2 1 1 0, 3 3
2 3 1 0, 3 3
2 4 1 0, 3 3
3 1 1 0, 3 3
3 2 1 0, 3 3
3 4 1 0, 3 3
4 2 1 0, 5
4 3 1 0, 5
定义空间联系 – 空间权重
I d w x x x x S wij i jj
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Moran I (Z value) is
? positive,observations tend to be similar;
? negative,observations tend to be dissimilar;
? approximately zero,observations are arranged randomly over space,
Geary C,
? large C value (>>1),observations tend to be dissimilar;
? small C value (<<1) indicates that they tend to be similar,
Moran I,
C d n w w x x x xijj
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Geary C,
全程空间统计相关判别
Local Moran,I d w Z
i ij jj i
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Local Geary,C d w Z Z
i ij i jj i
n( ) ( )? ?
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2
? significant and negative if location i is
associated with relatively low values in
surrounding locations;
? significant and positive if location i is
associated with relatively high values of
the surrounding locations,
? significant and small Local Geary (t<0)
suggests a positive spatial association
(similarity);
? significant and large Local Geary (t>0)
suggests a negative spatial association
(dissimilarity),
局部空间相关判别
简单空间自回归模型,
Y = ?WY + ?
最小二乘法 (OLS)估计有偏且不一致,
? ? ? ?? ? ?^ ( )' ( ) ( )' ( )' ( ) ( )'? ? ?? ?Wy Wy Wy y Wy Wy Wy1 1
E ( )^? ??
空间过程模型的一般形式
where W1 and W2 are spatial weight matrices,? ~ N(0,?),
y W y X? ? ?? ? ?1
? ? ? ?? ?W 2
空间自回归模型
空间自回归模型定义
( ) ( )y W y? ? ? ?? ? ? ?y Wy? ? ?? ? ?
(1) 简单空间自回归模型,
y Wy X? ? ?? ? ?
(2) 空 间内生变量自相关模型,
( ) ( )y X W y X? ? ? ?? ? ? ?
(3) 空间误差项自相关模型
y=X?+? ?=?W?+?
空间自相关检验
Test for spatial error dependence,
? Moran I test,
I = e'e/e' ~ N(?i,?2i)
where e is a vector of OLS residuals and W is a spatial weight
matrix,
? Largange Multiplier Test,
Test for the substantive spatial dependence,LM e r r e We tr W W W( ) { ' / } / [ ' ] ~ ( )? ?? ?2 2 2 2 1
LM l a g e Wy W X b M W X b tr W W W( ) { ' / } / {( )' / [ ' ]} ~ ( )? ? ?? ? ?2 2 2 2 2 1
空间自回归模型异方差检验
C e I W I W e e I W I W e kR R U U? ? ? ? ? ?{ ' ( )' ( ) ' ( )' ( ) } / ~ ( )? ? ? ? ? ?2 2
Chow test,
H0,
H1,
y X? ?? ?
y X Xi
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? ?
??
?
??
?
??
?
??
?00 ?? ?
where ? is the ML estimate for the spatial parameter,
eR (eU) are the residuals for a restricted (unrestricted) regression,and
?2 is the estimate for the error variance for either the restricted model,
the unrestricted model or both,
空间模型参数估计
The log-likelihood function for the spatial model,
with ?_? = (Ay-X?)’?-1B(Ay-X?)
where A = I - ?W1,
B = I - ?W2,
? is an error covariance matrix,
?_? is a sum of squares of appropriately transformed error terms,
L n A B? ? ? ? ? ?( / ) l n ( ) ( / ) l n | | l n | | l n | | ( / ) '2 2 1 2 1 2? ? ??
数据随机分布假设, 所有空间观察值随即等概率分布
数据分布的异方差性,
? 空间数据分布特性
? 空间样本非随即采集
? 非一致的空间观察单位
通用 Gi(d) 统计量,
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通用 local Moran,
通用 local Geary,
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空间统计分析的异方差性与一般局部统计变量研究
?Identify the spatial structure of economic and demographic
forces (FEA,urban core,urban periphery and rural hinterland),
?Identify the spatial interactions (linkages) between urban
centers and their periphery rural areas,
?Evaluate the effects of local amenities (infrastructure,public
services,education and environment) on rural hinterland
population and employment change,
?Suggest alternative public policies for promoting rural growth
and development,
主要研究目标,
III,城乡发展联系的空间统计分析
空间区域定义划分
1,划分功能经济区 (FEAs),
- Each county should have a closer commuting linkage to all the counties of its
group as a whole than to any other group
- All member counties of each group are geographically integrated and within
its self- contained boundary,
- For FEA definition,there needs to be at least one central county in each
group,which is consistent with the urban core and rural hinterland concepts of
central place theory,
2,定义区域经济中心,
3,构造通勤指数,
4,递代收敛算法
I l C Ci j
j j i
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ki
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功能经济区的划分 -以美国南部为例
辨识局部空间增长模式
应用空间统计量 (local Morans and local Gearys)辩识核心 -郊围增长模
式的准则,
扩散型增长 (+ +),Rural growth is associated with rapid growth in the
economic core - low p-value of Ii and high p-value of Ci,
非中心化扩散 (- +),Rural growth is associated with slow growth in the
economic core - low p-value of Ii and low p-value of Ci,
倒流效应 (+ -),Economic core growth is associated with slow growth or
decline in the rural areas - high p-value of Ii and low p-value of Ci,
相对独立化 (?),Growth in rural areas is not closely associated with changes
in economic activity in the economic core - the local Moran and the local
Geary are not significant,
基于空间统计的中心 -郊围分析研究
空间增长模式辨识研究
城乡发展联系的空间模型研究
目标, 研究从城市中心向城郊及偏远乡村扩散或倒流效应
Carlino-Mills 模型, P* = f(E*|?p) and E* = g(P*|?e)
修正 Carlino-Mills 模型,
?P89 = ao+ ?l (*?P89) + al ?E89 + a2 P80 + a3 E80 + a4 (P80*CORE)
+ a5 (P80*FRINGE) + ci Fli + ul
?E89 = b0 + ?2 (*?E89) + bl ?P89 + b2 E80 + b3 P80 +b4 (E80*CORE)
+ b5 (E80*FRINGE) + ei F2i + u2
? ?P Z Z E Z Z E P Xi it i P it P i t? ? ? ? ? ? ? ?? ?( ) ( )_ _? ? ? ? ? ? ? ?1 2 1 3 2 4 5 1 6 2 11
? ?E Z Z P Z Z Z P E Xi it i E it E i t? ? ? ? ? ? ? ?? ?( ) ( )_ _? ? ? ? ? ? ? ?1 2 1 3 2 4 1 5 1 6 2 11
指标定义与变量选择 (1)
Dependent variables,
P8090(E8090)= Changes from 1980 to 1990 in total population (employment) in rural hinterland
tracts,
Explanatory variables,
P80(E80) = 1980 total population (employment) in rural hinterland tracts,
IWP80(IWE80) = 1980 total population (employment) of the tracts within 30 miles spatial distance
from the ith tract,which include the observation in the ith tract,W is the spatial weight matrix
defined by the 30 miles spatial distance between tracts,and {wij} is 1 if tract j is within 30 miles
distance from tract i,
IWP8090( IWE8090)= Changes from 1980 to 1990 in total population (employment) of the tracts within 30 miles spatial distance from the ith tract ( include the observation in the ith tract),
predicted from the first-stage of the 2SLS method,
Local amenities,
DIST = the spatial distance to the urban core (miles),
RSEW80 = the percentage of house with public sewer facilities (1980 census data),
WSL80 = the water/sewer line density (miles/miles2),
PHL80 = the highway density (miles/miles2),
POV80 = the percentage of people under the poverty level (1980 census data),
RHOU78 = the percentage of new houses built from 1970-1980,
DEC80C = the average percentage of people with associate college degree and above within 30
miles,
PUPTEA80 = the average ratio of pupils to teachers in high school (pupils/teachers)
指标定义与变量选择（２）
Backwash or Spread
The variables for the urban/rural linkage in the Urban Growth models,
IPOP1*P80 = the 1990/1980 population growth rates in the urban centers interacted with the
1980 population in rural hinterland tracts,
IPOP2*P80 = the 1990/1980 population growth rates in the periphery interacted with the 1980
population in rural hinterland tracts,
IPOP1*E80 = the 1990/1980 population growth rates in the urban centers interacted with the
1980 employment in rural hinterland tracts,
IPOP2*E80 = the 1990/1980 population growth rates in the periphery interacted with the 1980
employment in rural hinterland tracts,
The variables for the urban/rural linkage in the Urban Size models,
POP1*P80 = the 1980 total population in the urban centers interacted with the 1980 population in rural hinterland tracts,
POP2*P80 = the 1980 total population in the periphery interacted with the 1980 population in
rural hinterland tracts,
POP1*E80 = the 1980 total population in the urban centers interacted with the 1980 employment
in rural hinterland tracts,
POP2*E80 = the 1980 total population in the periphery interacted with the 1980 employment in
rural hinterland tracts,
空间回归模型估计结果
城乡发展联系影响分析
? 缺损数据
? 多维空间分析 - 3D 方差图模型
? 异方差分布 – 局部性分析 (局部空间统计量,局部权重模型 )
? 高级模型 –罗切斯特 模型,时空模型
? 空间统计与 GIS的集成以便于有效的数据交换
?空间统计图,属性数据和 GIS地图的动态显示
?空间数据分析与网络 GIS
IV,空间统计研究课题
新的命题挑战
? 空间发展理论 (空间定义,空间均衡理论和空间非均衡理
论 )
? 空间统计方法 (空间相关检验，空间聚类划分，局部统
计量的构造,局部模式判别分析,空间 -时间模型，非线性
空间模型,及罗切斯特模型 )
? 空间分析软件开发 (S-PLUS FOR ARCVIEW 和
SPACESTAT )
? 空间统计培训
关于空间数据的处理
? 空间数据的异方差性 (Heterogeneity in spatial data)
? 空间数据定义的边界效应 (Boundary effect)
? 空间数据定义的测度效应 (Scale effect)
? 空间数据缺值 (Missing data)
? 空间座标系统及权重的定义 (Spatial weights)
空间数据分析理论与方法
? 空间平衡和非平衡理论 (Spatial equilibrium theories
and unequilibrium theories)
? 探索性数据分析 (Exploratory spatial data analysis)
? 空间数据抽样 (Spatial sampling)
? 地理统计学 (Geostatistics,such as multivariates
variogram and kriging)
? 局部统计分析 (Local spatial statistics)
? 空间聚类分析 (Spatial cluster analysis)
? 空间数据显示 (Spatial data visualization - dynamic
visualization,statistical graphics,multi-dimensional
data visualization)
空间模型
? 空间计量线性模型的辨识和检验 ( Specification and tests of spatial
models)
? 时空模型 (Space-time models)
? 罗切斯特模型 ( Logistics model for categorical data)
? 空间局部加权模型 ( Spatially weighted regression model)
? 非线性空间计量模型 ( Non-linear spatial models)
- THE END -
Thank You!
介绍内容
? 经济学原理
? 空间统计学原理
? 城乡发展联系的理论与建模分析
? 相关研究方向
Understanding the Economic Spatial Systems
应用地理学
?新经济
-Knowledge
-Information
-Globalization
?新科技
-Internet
-GIS&RS
-Spatial analytical tools
?新方法
-ESDA
-Spatial stats and
models
-Simulation
经济学
经济地理学
空间统计学
GIS&RS
Ｉ．经济学原理－新经济地理学
关于空间经济理论 -空间聚集的外部经济效应
目标 - 研究地区,城市和国际经济中下列因素相互作用,
? 增长回报效率
? 运输成本
? 生产要素的流动 (人力,物力,资本 )
空间聚集效应 -空间联系要素的作用与影响
? 知识扩散
? 市场经济中专门化技能的优势
? 与规模较大的地区市场相关的到流和正向联系
交通成本
距离（至城市中心）
蔬菜
麦
牲口
Von Thunen 模型, 土地租金与土地利用
土地租金 (愿付价格 )
效用函数,
最小化 {d} f (生产成本 + 交通成本 )
人口
纺织城市 金融城市
城市规模和产业结构
效用
II,空间统计学原理
? 环境研究中空间地理位置等因素日益增长的的重要性
? 空间 -时间变化比较
? 景观变化
? 空间分析技术发展 (GIS,RS & GPS)
? 对更高级和复杂分析方法的要求
关于空间统计学及应用的研究动因
? Why spatial data is different from non-spatial
data? (spatial neighborhood)
? Statistical property for spatial data,
? Spatial dependence (autocorrelation)
? Heterogeneity
? Spatial trend (non-stationarity)
? Sensitive to spatial boundaries and spatial unit
(Country,County,Tract) Elevation,Major cities and Lat /
Long grid
Why Spatial is Special?
空间分析问题
? Is there any spatial cluster over space?
? Are spatial observations distributed randomly over
space?
? Are spatial observations correlated (autocorrelation)?
? Is there any spatial outlier?
? Is there any spatial trend?
? What is the interaction (statistically and theoretically)
between different variables?
? How to predict an unknown spatial value at a specific
location,
常规统计学与空间统计学的差异
常规统计学 空间统计学
? Data,Time-series data Spatial data (cross-sectional)
? Relationship,Time (yt-1,yt,yt+1) Topology (yi-1,yi,yi+1)
? Process,{Z(t),t?T} {Z(s;t),s?D(t),t?T}
? Model,Y = ?WY + ?
t = 1,2,3,… wi,j = 1 if i is adjacent to j
? - time-series ? - spatial autocorrelation
autocorrelation
ttt YY ?? ?? ? 1
?空间抽样
?探索性数据分析
? 空间非稳定性检验
?空间自相关与联系检验
? 模型模拟与预测
? 数据驱动分析 (探索性数据分析 )
? 全程统计量
? 局部统计量
? 模型驱动分析
?空间线性模型
? 时空模型
空间统计学研究课题
?地理统计数据,
试验与理论方差图
协方差图和相关方差图
一般和通用插值法
空间过程拟合
?点数据,
空间随机检验
Ripley‘s K- 函数
局部聚集强度
空间随机过程模拟合
?网格数据,
全程空间自回归系数
局部空间相关系数
空间回归模型
网格数据拟合
空间统计数据分析功能
?空间稳定性与非稳定性检验 (variogram,covariogram,
correlogram,boxplots,trend model,and statistic graphics)
Experimental Variogram,
?空间自相关检验 (Moran I,Geary C,joint counts,Largrange Multiplier,
and Likelihood Ratio Test)
Moran I,
?空间关联检验 (G statistics,and LISA)
Local Moran,G Statistics,
Local Geary,
? ?
? ?
?
?
??
??
? n
i
n
ij
ij
n
i
n
ij
jiij
wS
xxxxw
dI
2
))((
)(
?
?
?
??
n
ijj
j
n
ijj
jij
i
x
xw
dG
,
,)(
2'
1
)]()([|)(|2 1)( i
N
i
i
k
k xzxzhNh k?
?
? ???
?
?
? n
ij
jijii ZwZdI )(
2)()( ?
?
?? n
ij
jiiji ZZwdC
空间分布模式分析
? 定义准则, 理论与经验方法
?可达性 (roads,rivers,railways,airlines and Internet)
?经济联系 (commuter flows,migrations,trade flows)
?社会联系 (college admission,language)
?地理位置联系 (neighborhood,geographical distance)
?定义方法,
?二进制距阵
?行标准化距阵
?权重函数 (wij=f(x,y..))
1 2
3
4
R O W, I D C O L, I D W E I G H T A W E I G H T B
1 2 1 0, 5
1 3 1 0, 5
2 1 1 0, 3 3
2 3 1 0, 3 3
2 4 1 0, 3 3
3 1 1 0, 3 3
3 2 1 0, 3 3
3 4 1 0, 3 3
4 2 1 0, 5
4 3 1 0, 5
定义空间联系 – 空间权重
I d w x x x x S wij i jj
n
i
n
ijj
n
i
n( ) ( )( ) ( )? ? ?? ??? ??2
S n x xii
n2 21? ? ?? ( ) x
n xii
n?
?? ?
1
1
Moran I (Z value) is
? positive,observations tend to be similar;
? negative,observations tend to be dissimilar;
? approximately zero,observations are arranged randomly over space,
Geary C,
? large C value (>>1),observations tend to be dissimilar;
? small C value (<<1) indicates that they tend to be similar,
Moran I,
C d n w w x x x xijj
n
i
n
ij i jj
n
i
n
ii
n( ) ( ) ( ) { ( ) ( ) }? ? ? ? ??? ?? ?1 2 2 2
Geary C,
全程空间统计相关判别
Local Moran,I d w Z
i ij jj i
n( ) ?
??
Local Geary,C d w Z Z
i ij i jj i
n( ) ( )? ?
??
2
? significant and negative if location i is
associated with relatively low values in
surrounding locations;
? significant and positive if location i is
associated with relatively high values of
the surrounding locations,
? significant and small Local Geary (t<0)
suggests a positive spatial association
(similarity);
? significant and large Local Geary (t>0)
suggests a negative spatial association
(dissimilarity),
局部空间相关判别
简单空间自回归模型,
Y = ?WY + ?
最小二乘法 (OLS)估计有偏且不一致,
? ? ? ?? ? ?^ ( )' ( ) ( )' ( )' ( ) ( )'? ? ?? ?Wy Wy Wy y Wy Wy Wy1 1
E ( )^? ??
空间过程模型的一般形式
where W1 and W2 are spatial weight matrices,? ~ N(0,?),
y W y X? ? ?? ? ?1
? ? ? ?? ?W 2
空间自回归模型
空间自回归模型定义
( ) ( )y W y? ? ? ?? ? ? ?y Wy? ? ?? ? ?
(1) 简单空间自回归模型,
y Wy X? ? ?? ? ?
(2) 空 间内生变量自相关模型,
( ) ( )y X W y X? ? ? ?? ? ? ?
(3) 空间误差项自相关模型
y=X?+? ?=?W?+?
空间自相关检验
Test for spatial error dependence,
? Moran I test,
I = e'e/e' ~ N(?i,?2i)
where e is a vector of OLS residuals and W is a spatial weight
matrix,
? Largange Multiplier Test,
Test for the substantive spatial dependence,LM e r r e We tr W W W( ) { ' / } / [ ' ] ~ ( )? ?? ?2 2 2 2 1
LM l a g e Wy W X b M W X b tr W W W( ) { ' / } / {( )' / [ ' ]} ~ ( )? ? ?? ? ?2 2 2 2 2 1
空间自回归模型异方差检验
C e I W I W e e I W I W e kR R U U? ? ? ? ? ?{ ' ( )' ( ) ' ( )' ( ) } / ~ ( )? ? ? ? ? ?2 2
Chow test,
H0,
H1,
y X? ?? ?
y X Xi
j
i
j
? ?
??
?
??
?
??
?
??
?00 ?? ?
where ? is the ML estimate for the spatial parameter,
eR (eU) are the residuals for a restricted (unrestricted) regression,and
?2 is the estimate for the error variance for either the restricted model,
the unrestricted model or both,
空间模型参数估计
The log-likelihood function for the spatial model,
with ?_? = (Ay-X?)’?-1B(Ay-X?)
where A = I - ?W1,
B = I - ?W2,
? is an error covariance matrix,
?_? is a sum of squares of appropriately transformed error terms,
L n A B? ? ? ? ? ?( / ) l n ( ) ( / ) l n | | l n | | l n | | ( / ) '2 2 1 2 1 2? ? ??
数据随机分布假设, 所有空间观察值随即等概率分布
数据分布的异方差性,
? 空间数据分布特性
? 空间样本非随即采集
? 非一致的空间观察单位
通用 Gi(d) 统计量,
?
?
?
??
n
ijj
jj
n
ijj
jjij
i
xp
xpw
dG
,
,)(*
通用 local Moran,
通用 local Geary,
?
?
? n
ijj
jijii ZdZdI
,
)(* ?
?
? n
ijj
jijjijij pwpwd
,
/
?
?
?? n
ijj
jiiji ZZddC
,
2)()(*
空间统计分析的异方差性与一般局部统计变量研究
?Identify the spatial structure of economic and demographic
forces (FEA,urban core,urban periphery and rural hinterland),
?Identify the spatial interactions (linkages) between urban
centers and their periphery rural areas,
?Evaluate the effects of local amenities (infrastructure,public
services,education and environment) on rural hinterland
population and employment change,
?Suggest alternative public policies for promoting rural growth
and development,
主要研究目标,
III,城乡发展联系的空间统计分析
空间区域定义划分
1,划分功能经济区 (FEAs),
- Each county should have a closer commuting linkage to all the counties of its
group as a whole than to any other group
- All member counties of each group are geographically integrated and within
its self- contained boundary,
- For FEA definition,there needs to be at least one central county in each
group,which is consistent with the urban core and rural hinterland concepts of
central place theory,
2,定义区域经济中心,
3,构造通勤指数,
4,递代收敛算法
I l C Ci j
j j i
ml
i j
j j i
mt( )
,,
? ?
?
?
?? ?
iiCaI ?? m a x)( )m a x ()(
,,
ki
n
ikk
n
ikk
kiki CCCaIor ?
? ?
??? ? ???
功能经济区的划分 -以美国南部为例
辨识局部空间增长模式
应用空间统计量 (local Morans and local Gearys)辩识核心 -郊围增长模
式的准则,
扩散型增长 (+ +),Rural growth is associated with rapid growth in the
economic core - low p-value of Ii and high p-value of Ci,
非中心化扩散 (- +),Rural growth is associated with slow growth in the
economic core - low p-value of Ii and low p-value of Ci,
倒流效应 (+ -),Economic core growth is associated with slow growth or
decline in the rural areas - high p-value of Ii and low p-value of Ci,
相对独立化 (?),Growth in rural areas is not closely associated with changes
in economic activity in the economic core - the local Moran and the local
Geary are not significant,
基于空间统计的中心 -郊围分析研究
空间增长模式辨识研究
城乡发展联系的空间模型研究
目标, 研究从城市中心向城郊及偏远乡村扩散或倒流效应
Carlino-Mills 模型, P* = f(E*|?p) and E* = g(P*|?e)
修正 Carlino-Mills 模型,
?P89 = ao+ ?l (*?P89) + al ?E89 + a2 P80 + a3 E80 + a4 (P80*CORE)
+ a5 (P80*FRINGE) + ci Fli + ul
?E89 = b0 + ?2 (*?E89) + bl ?P89 + b2 E80 + b3 P80 +b4 (E80*CORE)
+ b5 (E80*FRINGE) + ei F2i + u2
? ?P Z Z E Z Z E P Xi it i P it P i t? ? ? ? ? ? ? ?? ?( ) ( )_ _? ? ? ? ? ? ? ?1 2 1 3 2 4 5 1 6 2 11
? ?E Z Z P Z Z Z P E Xi it i E it E i t? ? ? ? ? ? ? ?? ?( ) ( )_ _? ? ? ? ? ? ? ?1 2 1 3 2 4 1 5 1 6 2 11
指标定义与变量选择 (1)
Dependent variables,
P8090(E8090)= Changes from 1980 to 1990 in total population (employment) in rural hinterland
tracts,
Explanatory variables,
P80(E80) = 1980 total population (employment) in rural hinterland tracts,
IWP80(IWE80) = 1980 total population (employment) of the tracts within 30 miles spatial distance
from the ith tract,which include the observation in the ith tract,W is the spatial weight matrix
defined by the 30 miles spatial distance between tracts,and {wij} is 1 if tract j is within 30 miles
distance from tract i,
IWP8090( IWE8090)= Changes from 1980 to 1990 in total population (employment) of the tracts within 30 miles spatial distance from the ith tract ( include the observation in the ith tract),
predicted from the first-stage of the 2SLS method,
Local amenities,
DIST = the spatial distance to the urban core (miles),
RSEW80 = the percentage of house with public sewer facilities (1980 census data),
WSL80 = the water/sewer line density (miles/miles2),
PHL80 = the highway density (miles/miles2),
POV80 = the percentage of people under the poverty level (1980 census data),
RHOU78 = the percentage of new houses built from 1970-1980,
DEC80C = the average percentage of people with associate college degree and above within 30
miles,
PUPTEA80 = the average ratio of pupils to teachers in high school (pupils/teachers)
指标定义与变量选择（２）
Backwash or Spread
The variables for the urban/rural linkage in the Urban Growth models,
IPOP1*P80 = the 1990/1980 population growth rates in the urban centers interacted with the
1980 population in rural hinterland tracts,
IPOP2*P80 = the 1990/1980 population growth rates in the periphery interacted with the 1980
population in rural hinterland tracts,
IPOP1*E80 = the 1990/1980 population growth rates in the urban centers interacted with the
1980 employment in rural hinterland tracts,
IPOP2*E80 = the 1990/1980 population growth rates in the periphery interacted with the 1980
employment in rural hinterland tracts,
The variables for the urban/rural linkage in the Urban Size models,
POP1*P80 = the 1980 total population in the urban centers interacted with the 1980 population in rural hinterland tracts,
POP2*P80 = the 1980 total population in the periphery interacted with the 1980 population in
rural hinterland tracts,
POP1*E80 = the 1980 total population in the urban centers interacted with the 1980 employment
in rural hinterland tracts,
POP2*E80 = the 1980 total population in the periphery interacted with the 1980 employment in
rural hinterland tracts,
空间回归模型估计结果
城乡发展联系影响分析
? 缺损数据
? 多维空间分析 - 3D 方差图模型
? 异方差分布 – 局部性分析 (局部空间统计量,局部权重模型 )
? 高级模型 –罗切斯特 模型,时空模型
? 空间统计与 GIS的集成以便于有效的数据交换
?空间统计图,属性数据和 GIS地图的动态显示
?空间数据分析与网络 GIS
IV,空间统计研究课题
新的命题挑战
? 空间发展理论 (空间定义,空间均衡理论和空间非均衡理
论 )
? 空间统计方法 (空间相关检验，空间聚类划分，局部统
计量的构造,局部模式判别分析,空间 -时间模型，非线性
空间模型,及罗切斯特模型 )
? 空间分析软件开发 (S-PLUS FOR ARCVIEW 和
SPACESTAT )
? 空间统计培训
关于空间数据的处理
? 空间数据的异方差性 (Heterogeneity in spatial data)
? 空间数据定义的边界效应 (Boundary effect)
? 空间数据定义的测度效应 (Scale effect)
? 空间数据缺值 (Missing data)
? 空间座标系统及权重的定义 (Spatial weights)
空间数据分析理论与方法
? 空间平衡和非平衡理论 (Spatial equilibrium theories
and unequilibrium theories)
? 探索性数据分析 (Exploratory spatial data analysis)
? 空间数据抽样 (Spatial sampling)
? 地理统计学 (Geostatistics,such as multivariates
variogram and kriging)
? 局部统计分析 (Local spatial statistics)
? 空间聚类分析 (Spatial cluster analysis)
? 空间数据显示 (Spatial data visualization - dynamic
visualization,statistical graphics,multi-dimensional
data visualization)
空间模型
? 空间计量线性模型的辨识和检验 ( Specification and tests of spatial
models)
? 时空模型 (Space-time models)
? 罗切斯特模型 ( Logistics model for categorical data)
? 空间局部加权模型 ( Spatially weighted regression model)
? 非线性空间计量模型 ( Non-linear spatial models)
- THE END -
Thank You!
