代码拉取完成，页面将自动刷新
Suggested citation:
Mendez C. (2021). Spatial econometrics for cross-sectional data: Columbus crime example. DOI: 10.5281/zenodo.5151076. Notebook available at https://deepnote.com/@carlos-mendez/STATA-Spatial-cross-section-00WMK3sKQl-z6oVRkTQgCQ.
*========================================
* 高级计量经济学
*========================================
* 计量经济学服务中心
*-------------------------------------------------------------------------------
* 参考资料：
* 《初级计量经济学及Stata应用：Stata从入门到进阶》
* 《高级计量经济学及Stata应用：Stata回归分析与应用》
* 《量化社会科学方法》
* 《社会科学因果推断》
* 《面板数据计量分析方法》
* 《时间序列计量分析方法》
* 《高级计量经济学及Eviews应用》
* 《R、Python、Mtalab初高级教程》
* 《空间计量入门：空间计量在Geoda、GeodaSpace中的应用》
* 《零基础|轻松搞定空间计量：空间计量及GeoDa、Stata应用》
* 《空间计量第二部：空间计量及Matlab应用课程》
* 《空间计量第三部：空间计量及Stata应用课程》
* 《空间计量第四部：《空间计量及ArcGis应用课程》
* 《空间计量第五部：空间计量经济学》
* 《空间计量第六部：《空间计量及Python应用》
* 《空间计量第七部：《空间计量及R应用》
* 《空间计量第八部：《高级空间计量经济学》
*-------------------------------------------------------------------------------
* SPATIAL ECONOMETRICS with cross-sectional data (Before and after Stata 15)
* 工作路径设置Clean your environment
clear all
macro drop _all
set more off
cls
version 15
* Change working directory
* to the location of this .do file
* 下载安装外部命令
*Install packages
* ssc install spmap
* ssc install shp2dta
* ssc install sppack
* ssc install spregcs
*帮助文件查看
*help spatwmat
*help spreg
*help spmat
*help spregcs
*help spatreg
* Import and unzip data
copy "https://github.com/quarcs-lab/data-open/raw/master/Columbus/columbus/columbus.zip" columbus.zip, replace
unzipfile columbus.zip
* 使用shp2dta命令生成dta文件(dBase and coordinates)
shp2dta using "columbus.shp", database("columbusDbase.dta") coordinates("columbusCoor.dta") genid(id) replace
* 导入stata数据
use "columbusDbase.dta", clear
describe
* 绘图
*spmap CRIME using "columbusCoor.dta", id(id) legend(size(small) position(11)) clmethod(custom) clbreaks(0 15 30 45 60 75) fcolor(Blues) title("Property crimes per thousand households") note("Columbus, Ohio 1980 neighorhood data" "Source: Anselin (1988)")
*graph save "mapCrime.gph", replace
*graph export "mapCrime.png", replace
* 使用spmat命令生成权重矩阵
spmat contiguity Wqueen using "columbusCoor.dta", id(id)
spmat contiguity WqueenS using "columbusCoor.dta", id(id) normalize(row)
* 权重矩阵描述性分析
spmat summarize Wqueen
spmat summarize Wqueen, links
spmat summarize WqueenS
spmat summarize WqueenS, links
* 权重矩阵导出为Mata对象
spmat getmatrix Wqueen mataWqueen
spmat getmatrix WqueenS mataWqueenS
* Display Mata matrices
mata
mataWqueen
mataWqueenS
end
*** Export W matrix (created with spmat) to stata file (that is, .dta)
* Export weight matrix to .txt file (with no id column)
spmat export Wqueen using "Wqueen_fromStata_spmat.txt", noid replace
spmat export WqueenS using "WqueenS_fromStata_spmat.txt", noid replace
* Import .txt weight matrix and save it at .dta (stata) data file
import delimited "Wqueen_fromStata_spmat.txt", delimiter(space) rowrange(2) clear
save "Wqueen_fromStata_spmat.dta", replace
import delimited "WqueenS_fromStata_spmat.txt", delimiter(space) rowrange(2) clear
save "WqueenS_fromStata_spmat.dta", replace
* [IMPORTANT] Import .dta weight matrix with spatwmat package
spatwmat using "Wqueen_fromStata_spmat.dta", name(Wqueen_fromStata_spatwmat)
matrix list Wqueen_fromStata_spatwmat
* [IMPORTANT] Import .dta weight matrix with spatwmat package, standardize it, and store eigen values
spatwmat using "Wqueen_fromStata_spmat.dta", name(WqueenS_fromStata_spatwmat) eigenval(eWqueenS_fromStata_spatwmat) standardize
matrix list WqueenS_fromStata_spatwmat
* Import .dta weights matrix with spmatrix (official function from Stata15)
use "Wqueen_fromStata_spmat.dta", clear
gen id = _n
order id, first
spset id
spmatrix fromdata WqueenS_fromStata15 = v*, normalize(row) replace
spmatrix summarize WqueenS_fromStata15
* 全局Global Moran's I 检验
use "columbusDbase.dta", clear
spatgsa CRIME, w(WqueenS_fromStata_spatwmat) moran
* (0) OLS模型，没有空间滞后
use "columbusDbase.dta", clear
spset id
regress CRIME INC HOVAL
estat moran, errorlag(WqueenS_fromStata15)
* LM检验
reg CRIME INC HOVAL
spatdiag, weights(WqueenS_fromStata_spatwmat)
* (1) SAR/SLM: Spatial lag model (using 3 alternative packages)
* using spregress (official function from Stata 15)
use "Wqueen_fromStata_spmat.dta", clear
gen id = _n
order id, first
spset id
spmatrix fromdata WqueenS_fromStata15 = v*, normalize(row) replace
spmatrix summarize WqueenS_fromStata15
use "columbusDbase.dta", clear
spset id
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) vce(robust)
estat ic
estat impact
* using the spregcs package (BE CAREFUL!! it requires a W created with spmat)
spregcs CRIME INC HOVAL, wmfile("Wqueen_fromStata_spmat.dta") model(sar) mfx(lin)
* using the spatreg package (BE CAREFUL!! it requires a W created with spatwmat)
spatreg CRIME INC HOVAL, weights(WqueenS_fromStata_spatwmat) eigenval(eWqueenS_fromStata_spatwmat) model(lag)
* (2) SEM: Spatial error model (using 3 alternative packages)
* using spregress (official function from Stata 15)
use "Wqueen_fromStata_spmat.dta", clear
gen id = _n
order id, first
spset id
spmatrix fromdata WqueenS_fromStata15 = v*, normalize(row) replace
spmatrix summarize WqueenS_fromStata15
use "columbusDbase.dta", clear
spset id
spregress CRIME INC HOVAL, ml errorlag(WqueenS_fromStata15) vce(robust)
estat ic
estat impact
* using the spregcs package (BE CAREFUL!! it requires a W created with spmat)
spregcs CRIME INC HOVAL, wmfile("Wqueen_fromStata_spmat.dta") model(sem) mfx(lin)
* using the spatreg package (BE CAREFUL!! it requires a W created with spatwmat)
spatreg CRIME INC HOVAL, weights(WqueenS_fromStata_spatwmat) eigenval(eWqueenS_fromStata_spatwmat) model(error)
* (3) Fit SLX model: spatial lag of the independent variables
use "Wqueen_fromStata_spmat.dta", clear
gen id = _n
order id, first
spset id
spmatrix fromdata WqueenS_fromStata15 = v*, normalize(row) replace
spmatrix summarize WqueenS_fromStata15
use "columbusDbase.dta", clear
spset id
spregress CRIME INC HOVAL, ml ivarlag(WqueenS_fromStata15: INC HOVAL) vce(robust)
estat ic
estat impact
* (4) Fit SAC model: spatial lag of the dependent and error term
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL) vce(robust)
estat ic
estat impact
* (5) Fit SDM model: spatial lag of the dependent and independent variables
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) errorlag(WqueenS_fromStata15) vce(robust)
estat ic
estat impact
* (6) Fit SDEM model: spatial lag of the independent variables and error term
spregress CRIME INC HOVAL, ml ivarlag(WqueenS_fromStata15: INC HOVAL) errorlag(WqueenS_fromStata15) vce(robust)
estat ic
estat impact
* (7) Fit GNS model: spatial lag of the dependent, independent, and error terms
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL) errorlag(WqueenS_fromStata15) vce(robust)
estat ic
estat impact
* Clean your environment
clear all
macro drop _all
set more off
*cls
*version 17
* Install packages: esttab, estadd, eststo, estout, estpost (http://repec.sowi.unibe.ch/stata/estout/index.html)
* net install st0085_2, from(http://www.stata-journal.com/software/sj14-2)
* ssc install estout, replace
Import W and data
* Import .dta weights matrix with spmatrix (official function from Stata15)
use "https://github.com/quarcs-lab/data-open/raw/master/Columbus/columbus/Wqueen_fromStata_spmat.dta", clear
gen id = _n
order id, first
spset id
spmatrix fromdata WqueenS_fromStata15 = v*, normalize(row) replace
spmatrix summarize WqueenS_fromStata15
Sp dataset: Wqueen_fromStata_spmat.dta
Linked shapefile: <none>
Data: Cross sectional
Spatial-unit ID: _ID (equal to id)
Coordinates: <none>
Weighting matrix WqueenS_fromStata15
---------------------------------------
Type | contiguity
Normalization | row
Dimension | 49 x 49
Elements |
minimum | 0
minimum > 0 | .1
mean | .0204082
max | .5
Neighbors |
minimum | 2
mean | 4.816327
maximum | 10
---------------------------------------
* Import the dataset and set up the spatial id: https://geodacenter.github.io/data-and-lab/columbus/
use "https://github.com/quarcs-lab/data-open/raw/master/Columbus/columbus/columbusDbase.dta", clear
spset id
Sp dataset: columbusDbase.dta
Linked shapefile: <none>
Data: Cross sectional
Spatial-unit ID: _ID (equal to id)
Coordinates: <none>
label var CRIME "Crime"
label var INC "Income"
label var HOVAL "House value"
OLS
regress CRIME INC HOVAL
eststo OLS
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
Source | SS df MS Number of obs = 49
-------------+---------------------------------- F(2, 46) = 28.39
Model | 7423.32674 2 3711.66337 Prob > F = 0.0000
Residual | 6014.89274 46 130.758538 R-squared = 0.5524
-------------+---------------------------------- Adj R-squared = 0.5329
Total | 13438.2195 48 279.962906 Root MSE = 11.435
------------------------------------------------------------------------------
CRIME | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
INC | -1.597311 .3341308 -4.78 0.000 -2.269881 -.9247405
HOVAL | -.2739315 .1031987 -2.65 0.011 -.4816597 -.0662033
_cons | 68.61896 4.735486 14.49 0.000 59.08692 78.151
------------------------------------------------------------------------------
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
OLS | 49 -207.0719 -187.3772 3 380.7545 386.4299
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
Moran's I test
regress CRIME INC HOVAL
estat moran, errorlag(WqueenS_fromStata15)
Source | SS df MS Number of obs = 49
-------------+---------------------------------- F(2, 46) = 28.39
Model | 7423.32674 2 3711.66337 Prob > F = 0.0000
Residual | 6014.89274 46 130.758538 R-squared = 0.5524
-------------+---------------------------------- Adj R-squared = 0.5329
Total | 13438.2195 48 279.962906 Root MSE = 11.435
------------------------------------------------------------------------------
CRIME | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
INC | -1.597311 .3341308 -4.78 0.000 -2.269881 -.9247405
HOVAL | -.2739315 .1031987 -2.65 0.011 -.4816597 -.0662033
_cons | 68.61896 4.735486 14.49 0.000 59.08692 78.151
------------------------------------------------------------------------------
Moran test for spatial dependence
H0: Error terms are i.i.d.
Errorlags: WqueenS_fromStata15
chi2(1) = 5.21
Prob > chi2 = 0.0225
LM tests
spatwmat using "https://github.com/quarcs-lab/data-open/raw/master/Columbus/columbus/Wqueen_fromStata_spmat.dta", name(WqueenS_fromStata_spatwmat) eigenval(eWqueenS_fromStata_spatwmat) standardize
The following matrices have been created:
1. Imported binary weights matrix WqueenS_fromStata_spatwmat (row-standardized)
Dimension: 49x49
2. Eigenvalues matrix eWqueenS_fromStata_spatwmat
Dimension: 49x1
quietly reg CRIME INC HOVAL
spatdiag, weights(WqueenS_fromStata_spatwmat)
Diagnostic tests for spatial dependence in OLS regression
---------------------------------------------------------
Fitted model
------------------------------------------------------------
CRIME = INC + HOVAL
------------------------------------------------------------
Weights matrix
------------------------------------------------------------
Name: WqueenS_fromStata_spatwmat
Type: Imported (binary)
Row-standardized: Yes
------------------------------------------------------------
Diagnostics
------------------------------------------------------------
Test | Statistic df p-value
-------------------------------+----------------------------
Spatial error: |
Moran's I | 2.840 1 0.005
Lagrange multiplier | 5.206 1 0.023
Robust Lagrange multiplier | 0.044 1 0.834
|
Spatial lag: |
Lagrange multiplier | 8.898 1 0.003
Robust Lagrange multiplier | 3.736 1 0.053
------------------------------------------------------------
SAR
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15)
eststo SAR
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -182.69106
Iteration 1: log likelihood = -182.67397
Iteration 2: log likelihood = -182.67397
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -182.67397
Iteration 1: log likelihood = -182.67397 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(3) = 88.00
Prob > chi2 = 0.0000
Log likelihood = -182.67397 Pseudo R2 = 0.5806
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -1.048728 .3304297 -3.17 0.002 -1.696359 -.4010978
HOVAL | -.2663348 .0888474 -3.00 0.003 -.4404725 -.0921971
_cons | 45.60325 7.951826 5.73 0.000 30.01796 61.18854
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
CRIME | .4233254 .1255855 3.37 0.001 .1771824 .6694684
--------------+----------------------------------------------------------------
var(e.CRIME)| 96.85718 19.77581 64.91392 144.5193
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(1) = 11.36 Prob > chi2 = 0.0007
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
SAR | 49 . -182.674 5 375.3479 384.807
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -1.100895 .3302446 -3.33 0.001 -1.748163 -.4536279
HOVAL | -.2795832 .0935004 -2.99 0.003 -.4628406 -.0963258
-------------+----------------------------------------------------------------
indirect |
INC | -.7176833 .3163904 -2.27 0.023 -1.337797 -.0975695
HOVAL | -.1822627 .1083184 -1.68 0.092 -.3945629 .0300375
-------------+----------------------------------------------------------------
total |
INC | -1.818579 .5115003 -3.56 0.000 -2.821101 -.8160566
HOVAL | -.4618459 .1818435 -2.54 0.011 -.8182526 -.1054393
------------------------------------------------------------------------------
SEM
spregress CRIME INC HOVAL, ml errorlag(WqueenS_fromStata15)
eststo SEM
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -183.79112
Iteration 1: log likelihood = -183.7495
Iteration 2: log likelihood = -183.74943
Iteration 3: log likelihood = -183.74943
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -183.74943
Iteration 1: log likelihood = -183.74943 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(2) = 30.15
Prob > chi2 = 0.0000
Log likelihood = -183.74943 Pseudo R2 = 0.5362
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -.9573054 .3771546 -2.54 0.011 -1.696515 -.2180961
HOVAL | -.3045593 .0921607 -3.30 0.001 -.4851909 -.1239276
_cons | 60.27947 5.904297 10.21 0.000 48.70726 71.85168
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
e.CRIME | .5467529 .1575357 3.47 0.001 .2379886 .8555173
--------------+----------------------------------------------------------------
var(e.CRIME)| 97.67424 20.43916 64.81252 147.1977
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(1) = 12.05 Prob > chi2 = 0.0005
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
SEM | 49 . -183.7494 5 377.4989 386.958
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -.9573054 .3771546 -2.54 0.011 -1.696515 -.2180961
HOVAL | -.3045593 .0921607 -3.30 0.001 -.4851909 -.1239276
-------------+----------------------------------------------------------------
indirect |
INC | 0 (omitted)
HOVAL | 0 (omitted)
-------------+----------------------------------------------------------------
total |
INC | -.9573054 .3771546 -2.54 0.011 -1.696515 -.2180961
HOVAL | -.3045593 .0921607 -3.30 0.001 -.4851909 -.1239276
------------------------------------------------------------------------------
SLX
spregress CRIME INC HOVAL, ml ivarlag(WqueenS_fromStata15: INC HOVAL)
eststo SLX
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -183.9706
Iteration 1: log likelihood = -183.9706
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(4) = 76.80
Prob > chi2 = 0.0000
Log likelihood = -183.9706 Pseudo R2 = 0.6105
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -1.09739 .3542451 -3.10 0.002 -1.791698 -.4030821
HOVAL | -.2943898 .0963324 -3.06 0.002 -.4831978 -.1055817
_cons | 74.55343 6.363788 11.72 0.000 62.08063 87.02622
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
INC | -1.398746 .530778 -2.64 0.008 -2.439051 -.3584399
HOVAL | .214841 .1970276 1.09 0.276 -.171326 .6010079
--------------+----------------------------------------------------------------
var(e.CRIME)| 106.8181 21.5805 71.89125 158.7133
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(2) = 7.31 Prob > chi2 = 0.0259
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
SLX | 49 . -183.9706 6 379.9412 391.2921
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -1.09739 .3542451 -3.10 0.002 -1.791698 -.4030821
HOVAL | -.2943898 .0963324 -3.06 0.002 -.4831978 -.1055817
-------------+----------------------------------------------------------------
indirect |
INC | -1.398746 .530778 -2.64 0.008 -2.439051 -.3584399
HOVAL | .214841 .1970276 1.09 0.276 -.171326 .6010079
-------------+----------------------------------------------------------------
total |
INC | -2.496136 .4671431 -5.34 0.000 -3.411719 -1.580552
HOVAL | -.0795488 .1966064 -0.40 0.686 -.4648903 .3057926
------------------------------------------------------------------------------
SDM
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL)
eststo SDM
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -181.63946
Iteration 1: log likelihood = -181.63926
Iteration 2: log likelihood = -181.63925
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -181.63925
Iteration 1: log likelihood = -181.63925 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(5) = 93.47
Prob > chi2 = 0.0000
Log likelihood = -181.63925 Pseudo R2 = 0.6120
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -.9199061 .3395439 -2.71 0.007 -1.5854 -.2544122
HOVAL | -.2971294 .0900249 -3.30 0.001 -.473575 -.1206838
_cons | 44.32001 14.18338 3.12 0.002 16.5211 72.11892
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
INC | -.5839133 .6053402 -0.96 0.335 -1.770358 .6025317
HOVAL | .2576843 .1850135 1.39 0.164 -.1049356 .6203042
CRIME | .4034626 .1718368 2.35 0.019 .0666687 .7402564
--------------+----------------------------------------------------------------
var(e.CRIME)| 93.27224 19.17105 62.34442 139.5427
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(3) = 13.88 Prob > chi2 = 0.0031
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
SDM | 49 . -181.6393 7 377.2785 390.5213
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -1.024988 .3241534 -3.16 0.002 -1.660317 -.3896588
HOVAL | -.2819673 .0911938 -3.09 0.002 -.4607038 -.1032309
-------------+----------------------------------------------------------------
indirect |
INC | -1.495926 .6979787 -2.14 0.032 -2.863939 -.1279129
HOVAL | .215844 .2797595 0.77 0.440 -.3324746 .7641626
-------------+----------------------------------------------------------------
total |
INC | -2.520914 .7319696 -3.44 0.001 -3.955548 -1.08628
HOVAL | -.0661233 .308123 -0.21 0.830 -.6700333 .5377866
------------------------------------------------------------------------------
Wald tests
Reduce to OLS?
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL)
* Wald test: Reduce to OLS? (NO if p < 0.05 of the spatial terms)
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -181.63946
Iteration 1: log likelihood = -181.63926
Iteration 2: log likelihood = -181.63925
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -181.63925
Iteration 1: log likelihood = -181.63925 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(5) = 93.47
Prob > chi2 = 0.0000
Log likelihood = -181.63925 Pseudo R2 = 0.6120
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -.9199061 .3395439 -2.71 0.007 -1.5854 -.2544122
HOVAL | -.2971294 .0900249 -3.30 0.001 -.473575 -.1206838
_cons | 44.32001 14.18338 3.12 0.002 16.5211 72.11892
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
INC | -.5839133 .6053402 -0.96 0.335 -1.770358 .6025317
HOVAL | .2576843 .1850135 1.39 0.164 -.1049356 .6203042
CRIME | .4034626 .1718368 2.35 0.019 .0666687 .7402564
--------------+----------------------------------------------------------------
var(e.CRIME)| 93.27224 19.17105 62.34442 139.5427
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(3) = 13.88 Prob > chi2 = 0.0031
Reduce to SLX?
* Wald test: Reduce to SLX? (NO if p < 0.05)
test ([WqueenS_fromStata15]CRIME = 0)
( 1) [WqueenS_fromStata15]CRIME = 0
chi2( 1) = 5.51
Prob > chi2 = 0.0189
Reduce to SAR?
* Wald test: Reduce to SAR? (NO if p < 0.05)
test ([WqueenS_fromStata15]INC = 0) ([WqueenS_fromStata15]HOVAL = 0)
( 1) [WqueenS_fromStata15]INC = 0
( 2) [WqueenS_fromStata15]HOVAL = 0
chi2( 2) = 2.10
Prob > chi2 = 0.3494
Reduce to SEM?
* Wald test: Reduce to SEM? (NO if p < 0.05)
testnl ([WqueenS_fromStata15]INC = -[WqueenS_fromStata15]CRIME*[CRIME]INC) ([WqueenS_fromStata15]HOVAL = -[WqueenS_fromStata15]CRIME*[CRIME]HOVAL)
(1) [WqueenS_fromStata15]INC = -[WqueenS_fromStata15]CRIME*[CRIME]INC
(2) [WqueenS_fromStata15]HOVAL = -[WqueenS_fromStata15]CRIME*[CRIME]HOVAL
chi2(2) = 4.08
Prob > chi2 = 0.1300
SDEM
spregress CRIME INC HOVAL, ml ivarlag(WqueenS_fromStata15: INC HOVAL) errorlag(WqueenS_fromStata15)
eststo SDEM
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -181.7792
Iteration 1: log likelihood = -181.779
Iteration 2: log likelihood = -181.779
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -181.779
Iteration 1: log likelihood = -181.779 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(4) = 46.68
Prob > chi2 = 0.0000
Log likelihood = -181.779 Pseudo R2 = 0.6092
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -1.052259 .3233005 -3.25 0.001 -1.685916 -.4186011
HOVAL | -.2781741 .091165 -3.05 0.002 -.4568542 -.099494
_cons | 73.64508 8.761175 8.41 0.000 56.4735 90.81667
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
INC | -1.204876 .5860084 -2.06 0.040 -2.353431 -.0563208
HOVAL | .1312451 .2111476 0.62 0.534 -.2825966 .5450868
e.CRIME | .4035821 .1773581 2.28 0.023 .0559666 .7511976
--------------+----------------------------------------------------------------
var(e.CRIME)| 93.8033 19.30177 62.67113 140.4005
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(3) = 12.03 Prob > chi2 = 0.0073
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
SDEM | 49 . -181.779 7 377.558 390.8007
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -1.052259 .3233005 -3.25 0.001 -1.685916 -.4186011
HOVAL | -.2781741 .091165 -3.05 0.002 -.4568542 -.099494
-------------+----------------------------------------------------------------
indirect |
INC | -1.204876 .5860084 -2.06 0.040 -2.353431 -.0563208
HOVAL | .1312451 .2111476 0.62 0.534 -.2825966 .5450868
-------------+----------------------------------------------------------------
total |
INC | -2.257135 .6515178 -3.46 0.001 -3.534086 -.9801833
HOVAL | -.146929 .2403654 -0.61 0.541 -.6180365 .3241785
------------------------------------------------------------------------------
SAC
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) errorlag(WqueenS_fromStata15)
eststo SAC
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -182.57166
Iteration 1: log likelihood = -182.55505
Iteration 2: log likelihood = -182.55502
Iteration 3: log likelihood = -182.55502
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -182.55502
Iteration 1: log likelihood = -182.55502 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(3) = 57.82
Prob > chi2 = 0.0000
Log likelihood = -182.55502 Pseudo R2 = 0.5793
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -1.042749 .3357121 -3.11 0.002 -1.700733 -.3847656
HOVAL | -.2798409 .09405 -2.98 0.003 -.4641755 -.0955063
_cons | 47.91536 9.298756 5.15 0.000 29.69013 66.14058
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
CRIME | .3693743 .1792524 2.06 0.039 .0180459 .7207026
e.CRIME | .1464169 .2997182 0.49 0.625 -.44102 .7338538
--------------+----------------------------------------------------------------
var(e.CRIME)| 97.04344 19.77021 65.09608 144.6697
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(2) = 10.63 Prob > chi2 = 0.0049
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
SAC | 49 . -182.555 6 377.11 388.461
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -1.080454 .3399105 -3.18 0.001 -1.746666 -.4142414
HOVAL | -.2899596 .0958282 -3.03 0.002 -.4777794 -.1021397
-------------+----------------------------------------------------------------
indirect |
INC | -.5730615 .4220918 -1.36 0.175 -1.400346 .2542232
HOVAL | -.1537916 .1161114 -1.32 0.185 -.3813657 .0737826
-------------+----------------------------------------------------------------
total |
INC | -1.653515 .6169502 -2.68 0.007 -2.862715 -.4443151
HOVAL | -.4437511 .1749537 -2.54 0.011 -.7866542 -.1008481
------------------------------------------------------------------------------
GNS
spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL) errorlag(WqueenS_fromStata15)
eststo GNS
estat ic
mat s=r(S)
quietly estadd scalar AIC = s[1,5]
estat impact
(49 observations)
(49 observations (places) used)
(weighting matrix defines 49 places)
Performing grid search ... finished
Optimizing concentrated log likelihood:
Iteration 0: log likelihood = -181.60541
Iteration 1: log likelihood = -181.58046
Iteration 2: log likelihood = -181.58014
Iteration 3: log likelihood = -181.58014
Optimizing unconcentrated log likelihood:
Iteration 0: log likelihood = -181.58014
Iteration 1: log likelihood = -181.58014 (backed up)
Spatial autoregressive model Number of obs = 49
Maximum likelihood estimates Wald chi2(5) = 62.57
Prob > chi2 = 0.0000
Log likelihood = -181.58014 Pseudo R2 = 0.6115
-------------------------------------------------------------------------------
CRIME | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
CRIME |
INC | -.9587964 .3565186 -2.69 0.007 -1.65756 -.2600328
HOVAL | -.2890341 .0924525 -3.13 0.002 -.4702378 -.1078305
_cons | 53.04797 31.4573 1.69 0.092 -8.607201 114.7031
--------------+----------------------------------------------------------------
WqueenS_fr~15 |
INC | -.7734089 .8571065 -0.90 0.367 -2.453307 .906489
HOVAL | .2184638 .2304209 0.95 0.343 -.2331529 .6700806
CRIME | .284377 .4183839 0.68 0.497 -.5356404 1.104394
e.CRIME | .1632527 .4661928 0.35 0.726 -.7504684 1.076974
--------------+----------------------------------------------------------------
var(e.CRIME)| 94.48532 19.32815 63.27621 141.0874
-------------------------------------------------------------------------------
Wald test of spatial terms: chi2(4) = 12.51 Prob > chi2 = 0.0139
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
GNS | 49 . -181.5801 8 379.1603 394.2948
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.
progress : 50% 100%
Average impacts Number of obs = 49
------------------------------------------------------------------------------
| Delta-Method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
direct |
INC | -1.032865 .3233102 -3.19 0.001 -1.666541 -.3991884
HOVAL | -.2793854 .091442 -3.06 0.002 -.4586084 -.1001624
-------------+----------------------------------------------------------------
indirect |
INC | -1.387691 .7255571 -1.91 0.056 -2.809757 .0343749
HOVAL | .1807716 .2720029 0.66 0.506 -.3523444 .7138875
-------------+----------------------------------------------------------------
total |
INC | -2.420556 .7598804 -3.19 0.001 -3.909894 -.9312175
HOVAL | -.0986138 .2989642 -0.33 0.742 -.6845729 .4873452
------------------------------------------------------------------------------
Comparison
%html
esttab OLS SAR SEM SLX SDM SDEM SAC GNS, label stats(AIC) mtitle("OLS" "SAR" "SEM" "SLX" "SDM" "SDEM" "SAC" "GNS") html
(1) (2) (3) (4) (5) (6) (7) (8)
OLS SAR SEM SLX SDM SDEM SAC GNS
main
Income -1.597*** -1.049** -0.957* -1.097** -0.920** -1.052** -1.043** -0.959**
(-4.78) (-3.17) (-2.54) (-3.10) (-2.71) (-3.25) (-3.11) (-2.69)
House value -0.274* -0.266** -0.305*** -0.294** -0.297*** -0.278** -0.280** -0.289**
(-2.65) (-3.00) (-3.30) (-3.06) (-3.30) (-3.05) (-2.98) (-3.13)
Constant 68.62*** 45.60*** 60.28*** 74.55*** 44.32** 73.65*** 47.92*** 53.05
(14.49) (5.73) (10.21) (11.72) (3.12) (8.41) (5.15) (1.69)
WqueenS_fromStata15
Crime 0.423*** 0.403* 0.369* 0.284
(3.37) (2.35) (2.06) (0.68)
e.Crime 0.547*** 0.404* 0.146 0.163
(3.47) (2.28) (0.49) (0.35)
Income -1.399** -0.584 -1.205* -0.773
(-2.64) (-0.96) (-2.06) (-0.90)
House value 0.215 0.258 0.131 0.218
(1.09) (1.39) (0.62) (0.95)
/
var(e.CRIME) 96.86*** 97.67*** 106.8*** 93.27*** 93.80*** 97.04*** 94.49***
(4.90) (4.78) (4.95) (4.87) (4.86) (4.91) (4.89)
AIC 380.8 375.3 377.5 379.9 377.3 377.6 377.1 379.2
t statistics in parentheses
* p < 0.05, ** p < 0.01, *** p < 0.001
eststo clear
The following comparison requires Stata 17. Caution is needed as the p-values are not shown
collect clear
quietly spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15)
collect: quietly estat impact
quietly spregress CRIME INC HOVAL, ml ivarlag(WqueenS_fromStata15: INC HOVAL)
collect: quietly estat impact
quietly spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL)
collect: quietly estat impact
quietly spregress CRIME INC HOVAL, ml ivarlag(WqueenS_fromStata15: INC HOVAL) errorlag(WqueenS_fromStata15)
collect: quietly estat impact
quietly spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) errorlag(WqueenS_fromStata15)
collect: quietly estat impact
quietly spregress CRIME INC HOVAL, ml dvarlag(WqueenS_fromStata15) ivarlag(WqueenS_fromStata15: INC HOVAL) errorlag(WqueenS_fromStata15)
collect: quietly estat impact
collect label list cmdset, all
collect style autolevels result b_direct b_indirect
collect label levels cmdset 1 "SAR" 2 "SLX" 3 "SDM" 4 "SDEM" 5 "SAC" 6 "GNS"
collect style cell, nformat(%7.2f)
collect layout (colname#result) (cmdset)
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