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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
* 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 .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"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.
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
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) standardizeThe 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
------------------------------------------------------------
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
------------------------------------------------------------------------------
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
------------------------------------------------------------------------------
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
------------------------------------------------------------------------------
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
------------------------------------------------------------------------------
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
* 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
* 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
* 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
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
------------------------------------------------------------------------------
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
------------------------------------------------------------------------------
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
------------------------------------------------------------------------------
%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 clearThe 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)
Collection: default
Dimension: cmdset
Label: Command results index
Level labels:
1
2
3
4
5
6
Collection: default
Rows: colname#result
Columns: cmdset
Table 1: 6 x 6
--------------------------------------------------
| SAR SLX SDM SDEM SAC GNS
-------------+------------------------------------
Income |
b_direct | -1.10 -1.10 -1.02 -1.05 -1.08 -1.03
b_indirect | -0.72 -1.40 -1.50 -1.20 -0.57 -1.39
House value |
b_direct | -0.28 -0.29 -0.28 -0.28 -0.29 -0.28
b_indirect | -0.18 0.21 0.22 0.13 -0.15 0.18
--------------------------------------------------
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