# tutorial-spatial-cross-section-columbus-crime **Repository Path**: fangyebing/tutorial-spatial-cross-section-columbus-crime ## Basic Information - **Project Name**: tutorial-spatial-cross-section-columbus-crime - **Description**: 空间计量操作指南（columbus数据） - **Primary Language**: Unknown - **License**: Not specified - **Default Branch**: main - **Homepage**: None - **GVP Project**: No ## Statistics - **Stars**: 0 - **Forks**: 2 - **Created**: 2022-10-18 - **Last Updated**: 2022-10-18 ## Categories & Tags **Categories**: Uncategorized **Tags**: None ## README ## Tutorial : Spatial econometrics for cross-sectional data (Columbus crime example) [![DOI](https://zenodo.org/badge/387109687.svg)](https://zenodo.org/badge/latestdoi/387109687) Suggested citation: > Mendez C. (2021). Spatial econometrics for cross-sectional data: Columbus crime example. DOI: [10.5281/zenodo.5151076](https://doi.org/10.5281/zenodo.5151076). Notebook available at https://deepnote.com/@carlos-mendez/STATA-Spatial-cross-section-00WMK3sKQl-z6oVRkTQgCQ. # 空间计量教程：Python+Stata操作代码 # Stata操作代码 ``` *======================================== * 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 ``` # 操作结果为 ``` * 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: Data: Cross sectional Spatial-unit ID: _ID (equal to id) Coordinates: 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: Data: Cross sectional Spatial-unit ID: _ID (equal to id) Coordinates: 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) ```