+-------+ ----+ Title +------------------------------------------------------------
spmstar: (m-STAR) Multiparametric Spatio Temporal AutoRegressive Regression (Spatial Lag Cross Sections Models)
+-------------------+ ----+ Table of Contents +------------------------------------------------
Syntax Description Options Saved Results References
*** Examples
Author
+--------+ ----+ Syntax +-----------------------------------------------------------
spmstar depvar indepvars [weight] , wmfile(weight_file) nwmat(#) noconstant [ dist(norm|weib) mfx(lin, log) stand inv inv2 tolog nolog robust coll zero predict(new_var) resid(new_var) iter(#) tech(name) tobit ll(real 0) level(#) vce(vcetype) maximize other maximization options ]
+-------------+ ----+ Description +------------------------------------------------------
spmstar estimates Spatial econometric regression (MSTAR) "Multiparametric Spatio Temporal AutoRegressive Regression" for Spatial Lag Cross Sections Models.
spmstar estimates Continuous and Truncated Dependent Variables models tobit.
spmstar deals with data either continuous or truncated dependent variable. If depvar has missing values or lower limits, so in this case spmstar will fit spatial cross section model via tobit model, and thus spmstar can resolve the problem of missing values that exist in many kinds of data. Otherwise, in the case of continuous data, the normal estimation will be used.
spmstar can generate: - Binary / Standardized Weight Matrix. - Inverse / Inverse Squared Standardized Weight Matrix. - Binary / Standardized / Inverse Eigenvalues Variable.
spmstar predicted values are obtained from conditional expectation expression.
Yh = E(y|x) = inv(I-Rho*W) * X*Beta
R2, R2 Adjusted, and F-Test, are obtained from 4 ways: 1- (Buse 1973) R2. 2- Raw Moments R2. 3- squared correlation between predicted (Yh) and observed dependent variable (Y). 4- Ratio of variance between predicted (Yh) and observed dependent variable (Y).
- Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1). - F-Test=R2/(1-R2)*(N-K-1)/(K).
*** Important Notes: spmstar generates some variables names with prefix: w1x_ , w2x_ , w3x_ , w4x_ , w1y_ , w2y_ , mstar_ , spat_ So, you must avoid to include variables names with thes prefixes
+---------+ ----+ Options +----------------------------------------------------------
wmfile(weight_file) Open CROSS SECTION weight matrix file.
Spatial Cross Sections Weight Matrix file must be: 1- Square Matrix [NxN] 2- Symmetric Matrix (Optional)
Spatial Weight Matrix has two types: Standardized and binary weight matrix.
stand Use Standardized Weight Matrix, (each row sum equals 1) Default is Binary spatial Weight Matrix which each element i > s 0 or 1
inv Use Inverse Standardized Weight Matrix (1/W)
inv2 Use Inverse Squared Standardized Weight Matrix (1/W^2)
spmstar is used with more than Weight Matrix: (Border, Language, Currency, Trade...)
zero convert missing values observations to Zero
nwmat(1,2,3,4) number of Rho's matrixes to be used
coll keep collinear variables; default is removing collinear vari > ables.
noconstant Exclude Constant Term from Equation
nolog suppress iteration of the log likelihood
tobit Estimate model via Tobit regression
ll(#) value of minimum left-censoring dependent variable with: (tobit); default is 0
mfx(lin, log) functional form: Linear model (lin), or Log-Log model (log), to compute Total, Direct, and InDirect Marginal Effects and > Elasticities - In Linear model: marginal effects are the coefficients (Bm), and elasticities are (Es = Bm X/Y). - In Log-Log model: elasticities are the coefficients (Es), and the marginal effects are (Bm = Es Y/X). - mfx(log) and tolog options must be combined, to transform linear variables > to log form.
mfx(lin, log) can calculate: - Total Marginal Effects and Elasticities. - Direct Marginal Effects and Elasticities. - InDirect Marginal Effects and Elasticities.
tolog Convert dependent and independent variables to LOG Form in the memory for Log-Log regression. tolog Transforms depvar and indepvars to Log Form without lost the original data variables
dist(norm, weib) Distribution of error term: 1- dist(norm) Normal distribution; default. 3- dist(weib) Weibull distribution.
dist option is used to remedy non normality problem, when the error term has non normality distribution. dist(weib) can be used.
dist(norm) is the default distribution.
predict(new_variable) Predicted values variable
resid(new_variable) Residuals values variable computed as Ue=Y-Yh
robust Huber-White standard errors
tech(name) technique algorithm for maximization of the log likelihood f > unction LLF tech(nr) Newton-Raphson (NR) algorithm; default tech(bhhh) Berndt-Hall-Hall-Hausman (BHHH) algorithm tech(dfp) Davidon-Fletcher-Powell (DFP) algorithm tech(bfgs) Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm
iter(#) maximum iterations; default is 100 if iter(#) is reached (100), this means convergence not ach > ieved yet, so you can use another technique algorithm to converge LLF > function or exceed number of maximum iterations more than 100.
vce(vcetype) ols, robust, cluster, bootstrap, jackknife, hc2, hc3
level(#) confidence intervals level; default is level(95)
Other maximization_options allows the user to specify other maximization options (e.g., difficult, trace, iterate(#), etc.). However, you should rarely have to specify them, though they may be helpful if parameters approach boundary values.
+---------------+ ----+ Saved Results +----------------------------------------------------
spmstar saves the following results in e():
Scalars
e(N) number of observations e(r2bu) R-squared (Buse 1973) e(r2bu_a) R-squared Adj (Buse 1973) e(r2raw) Raw Moments R2 e(r2raw_a) Raw Moments R2 Adj e(f) F-test e(fp) F-test P-Value e(wald) Wald-test e(waldp) Wald-test P-Value e(r2h) R2 Between Predicted (Yh) and Observed DepVar (Y) e(r2h_a) Adjusted r2h e(fh) F-test due to r2h e(fhp) F-test due to r2h P-Value e(r2v) R2 Variance Ratio Between Predicted (Yh) and Observed DepVar > (Y) e(r2v_a) Adjusted r2v e(fv) F-test due to r2v e(fvp) F-test due to r2v P-Value e(sig) Root MSE (Sigma) e(llf) Log Likelihood Function
Matrixes e(b) coefficient vector e(V) variance-covariance matrix of the estimators
e(mfxlinb) Beta, Total, Direct, and InDirect Marginal Effect (in Lin Fo > rm) e(mfxline) Beta, Total, Direct, and InDirect Elasticity (in Lin Fo > rm)
e(mfxlogb) Beta, Total, Direct, and InDirect Marginal Effect (in Log Fo > rm) e(mfxloge) Beta, Total, Direct, and InDirect Elasticity (in Log Fo > rm)
Functions e(sample) marks estimation sample
+------------+ ----+ References +-------------------------------------------------------
Anselin, L. (2001) "Spatial Econometrics", In Baltagi, B. (Ed).: A Companion to Theoretical Econometrics Basil Blackwell: Oxford, UK.
Anselin, L. (2007) "Spatial Econometrics", In T. C. Mills and K. Patterson (Eds).: Palgrave Handbook of Econometrics. Vol 1, Econometric Theory. New York: Palgrave MacMillan.
Anselin, L. & Florax RJ. (1995) "New Directions in Spatial Econometrics: Introduction. In New Directions in Spatial Econometrics", Anselin L, Florax RJ (eds). Berlin, Germany: Springer-Verlag.
Hays, Jude C., Aya Kachi & Robert J. Franzese, Jr (2010) "A Spatial Model Incorporating Dynamic, Endogenous Network Interdependence: A Political Science Application", Statistical Methodology 7(3); 406-428.
James LeSage and R. Kelly Pace (2009) "Introduction to Spatial Econometrics", Publisher: Chapman & Hall/CRC.
+----------+ ----+ Examples +---------------------------------------------------------
Note 1: you can use: spweight, spweightcs, spweightxt to create Spatial Weight > Matrix. Note 2: Remember, your spatial weight matrix must be: *** 1-Cross Section Dimention 2- Square Matrix 3- Symmetric Matrix Note 3: You can use the dialog box for spmstar. -------------------------------------------------------------------------------
clear all
sysuse spmstar.dta, clear
* (m-STAR) Multiparametric Spatio Temporal AutoRegressive Regression * (m-STAR) Lag Model
*** YOU MUST HAVE DIFFERENT Weighted Matrixes Files:
* (1) *** Normal Distribution spmstar y x1 x2 , wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(norm) spmstar y x1 x2 , wmfile(SPWmcs2) nwmat(2) mfx(lin) dist(norm) spmstar y x1 x2 , wmfile(SPWmcs3) nwmat(3) mfx(lin) dist(norm) spmstar y x1 x2 , wmfile(SPWmcs4) nwmat(4) mfx(lin) dist(norm) spmstar ys x1 x2, wmfile(SPWmcs4) nwmat(4) mfx(lin) dist(norm) tobit ll(0) spmstar ys x1 x2, wmfile(SPWmcs4) nwmat(4) mfx(lin) dist(norm) tobit ll(3) -------------------------------------------------------------------------------
* (2) *** Weibull Distribution spmstar y x1 x2 , wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(weib) spmstar y x1 x2 , wmfile(SPWmcs2) nwmat(2) mfx(lin) dist(weib) spmstar y x1 x2 , wmfile(SPWmcs3) nwmat(3) mfx(lin) dist(weib) spmstar y x1 x2 , wmfile(SPWmcs4) nwmat(4) mfx(lin) dist(weib) spmstar ys x1 x2, wmfile(SPWmcs4) nwmat(4) mfx(lin) dist(weib) tobit ll(0) spmstar ys x1 x2, wmfile(SPWmcs4) nwmat(4) mfx(lin) dist(weib) tobit ll(3) -------------------------------------------------------------------------------
* (3) Weighted mSTAR Normal Distribution: spmstar y x1 x2 [weight = x1], wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(norm) spmstar y x1 x2 [aweight = x1], wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(norm) spmstar y x1 x2 [iweight = x1], wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(norm) -------------------------------------------------------------------------------
* (4) Weighted mSTAR Weibull Distribution: spmstar y x1 x2 [weight = x1], wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(weib) spmstar y x1 x2 [aweight = x1], wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(weib) spmstar y x1 x2 [iweight = x1], wmfile(SPWmcs1) nwmat(1) mfx(lin) dist(weib) -------------------------------------------------------------------------------
. clear all . sysuse spmstar.dta, clear . spmstar y x1 x2 , wmfile(SPWmcs1) nwmat(1) dist(norm) mfx(lin)
============================================================================== *** Binary (0/1) Weight Matrix: 49x49 (Non Normalized) ============================================================================== ============================================================================== * MLE Multiparametric Spatio Temporal AutoRegressive Regression * (m-STAR) Spatial Lag Normal Model (1 Weight Matrix) ============================================================================== y = x1 + x2 ------------------------------------------------------------------------------ Sample Size = 49 Wald Test = 56.4471 | P-Value > Chi2(2) = 0.0000 F-Test = 28.2236 | P-Value > F(2 , 47) = 0.0000 (Buse 1973) R2 = 0.5510 | Raw Moments R2 = 0.9184 (Buse 1973) R2 Adj = 0.5414 | Raw Moments R2 Adj = 0.9166 Root MSE (Sigma) = 11.3305 | Log Likelihood Function = -186.8161 ------------------------------------------------------------------------------ - R2h= 0.5510 R2h Adj= 0.5415 F-Test = 28.23 P-Value > F(2 , 47) 0.0000 - R2v= 0.5543 R2v Adj= 0.5448 F-Test = 28.61 P-Value > F(2 , 47) 0.0000 ------------------------------------------------------------------------------ - Sum of Rho's = 0.0211161 Sum must be < 1 for Stability Condition ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y | x1 | -.252788 .1007052 -2.51 0.012 -.4501667 -.0554094 x2 | -1.585978 .3198759 -4.96 0.000 -2.212924 -.959033 _cons | 64.04514 6.233457 10.27 0.000 51.82779 76.26249 -------------+---------------------------------------------------------------- Rho1 | .0211161 .0197638 1.07 0.285 -.0176202 .0598524 Sigma | 10.94111 1.10546 9.90 0.000 8.774445 13.10777 ------------------------------------------------------------------------------ Wald Test [Rho1=0]: 1.1415 P-Value > Chi2(1) 0.2853 Acceptable Range for Rho1: -0.3199 < Rho1 < 0.1633 ------------------------------------------------------------------------------
* Beta, Total, Direct, and InDirect Linear: Marginal Effect *
+--------------------------------------------------------------------------+ | Variable | Beta(B) | Total | Direct | InDirect | Mean | |--------------+-----------+-----------+-----------+-----------+-----------| |y | | | | | | | x1 | -0.2528 | -0.2522 | -0.2266 | -0.0256 | 38.4362 | | x2 | -1.5860 | -1.5824 | -1.4218 | -0.1606 | 14.3749 | +--------------------------------------------------------------------------+
* Beta, Total, Direct, and InDirect Linear: Elasticity *
+--------------------------------------------------------------------------+ | Variable | Beta(Es) | Total | Direct | InDirect | Mean | |--------------+-----------+-----------+-----------+-----------+-----------| | x1 | -0.2766 | -0.2760 | -0.2480 | -0.0280 | 38.4362 | | x2 | -0.6490 | -0.6475 | -0.5818 | -0.0657 | 14.3749 | +--------------------------------------------------------------------------+ Mean of Dependent Variable = 35.1288
+--------+ ----+ Author +-----------------------------------------------------------
Emad Abd Elmessih Shehata Professor (PhD Economics) Agricultural Research Center - Agricultural Economics Research Institute - Eg > ypt Email: emadstat@hotmail.com WebPage: http://emadstat.110mb.com/stata.htm WebPage at IDEAS: http://ideas.repec.org/f/psh494.html WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm
+------------------+ ----+ SPMSTAR Citation +-------------------------------------------------
Shehata, Emad Abd Elmessih (2012) SPMSTAR: "(m-STAR) Spatial Multiparametric Spatio Temporal AutoRegressive Regression: Spatial Lag Cross Sections Models"
http://ideas.repec.org/c/boc/bocode/s457379.html
http://econpapers.repec.org/software/bocbocode/s457379.htm
Online Help:
*** Spatial Econometrics Regression Models:
------------------------------------------------------------------------------- > - *** (1) Spatial Panel Data Regression Models: spregxt Spatial Panel Regression Econometric Models: Stata Module Toolkit gs2slsxt Generalized Spatial Panel 2SLS Regression gs2slsarxt Generalized Spatial Panel Autoregressive 2SLS Regression spglsxt Spatial Panel Autoregressive Generalized Least Squares Regression spgmmxt Spatial Panel Autoregressive Generalized Method of Moments Regress > ion spmstarxt (m-STAR) Spatial Lag Panel Models spmstardxt (m-STAR) Spatial Durbin Panel Models spmstardhxt (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Panel Mo > dels spmstarhxt (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Panel Model > s spregdhp Spatial Panel Han-Philips Linear Dynamic Regression: Lag & Durbin > Models spregdpd Spatial Panel Arellano-Bond Linear Dynamic Regression: Lag & Durbi > n Models spregfext Spatial Panel Fixed Effects Regression: Lag & Durbin Models spregrext Spatial Panel Random Effects Regression: Lag & Durbin Models spregsacxt MLE Spatial AutoCorrelation Panel Regression (SAC) spregsarxt MLE Spatial Lag Panel Regression (SAR) spregsdmxt MLE Spatial Durbin Panel Regression (SDM) spregsemxt MLE Spatial Error Panel Regression (SEM) ------------------------------------------------------------------------------- > - *** (2) Spatial Cross Section Regression Models: spregcs Spatial Cross Section Regression Econometric Models: Stata Module > Toolkit gs2sls Generalized Spatial 2SLS Cross Sections Regression gs2slsar Generalized Spatial Autoregressive 2SLS Cross Sections Regression gs3sls Generalized Spatial Autoregressive 3SLS Regression gs3slsar Generalized Spatial Autoregressive 3SLS Cross Sections Regression gsp3sls Generalized Spatial 3SLS Cross Sections Regression spautoreg Spatial Cross Section Regression Models spgmm Spatial Autoregressive GMM Cross Sections Regression spmstar (m-STAR) Spatial Lag Cross Sections Models spmstard (m-STAR) Spatial Durbin Cross Sections Models spmstardh (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity Cross Se > ctions Models spmstarh (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Cross Secti > ons Models spregsac MLE Spatial AutoCorrelation Cross Sections Regression (SAC) spregsar MLE Spatial Lag Cross Sections Regression (SAR) spregsdm MLE Spatial Durbin Cross Sections Regression (SDM) spregsem MLE Spatial Error Cross Sections Regression (SEM) ------------------------------------------------------------------------------- > - *** (3) Tobit Spatial Regression Models:
*** (3-1) Tobit Spatial Panel Data Regression Models: sptobitgmmxt Tobit Spatial GMM Panel Regression sptobitmstarxtTobit (m-STAR) Spatial Lag Panel Models sptobitmstardxtTobit (m-STAR) Spatial Durbin Panel Models sptobitmstardhxtTobit (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity > Panel Models sptobitmstarhxtTobit (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Pan > el Models sptobitsacxt Tobit MLE Spatial AutoCorrelation (SAC) Panel Regression sptobitsarxt Tobit MLE Spatial Lag Panel Regression sptobitsdmxt Tobit MLE Spatial Panel Durbin Regression sptobitsemxt Tobit MLE Spatial Error Panel Regression spxttobit Tobit Spatial Panel Autoregressive GLS Regression -------------------------------------------------------------- *** (3-2) Tobit Spatial Cross Section Regression Models: sptobitgmm Tobit Spatial GMM Cross Sections Regression sptobitmstar Tobit (m-STAR) Spatial Lag Cross Sections Models sptobitmstardTobit (m-STAR) Spatial Durbin Cross Sections Models sptobitmstardhTobit (m-STAR) Spatial Durbin Multiplicative Heteroscedasticity C > ross Sections sptobitmstarhTobit (m-STAR) Spatial Lag Multiplicative Heteroscedasticity Cross > Sections sptobitsac Tobit MLE AutoCorrelation (SAC) Cross Sections Regression sptobitsar Tobit MLE Spatial Lag Cross Sections Regression sptobitsdm Tobit MLE Spatial Durbin Cross Sections Regression sptobitsem Tobit MLE Spatial Error Cross Sections Regression ------------------------------------------------------------------------------- > - *** (4) Spatial Weight Matrix: spcs2xt Convert Cross Section to Panel Spatial Weight Matrix spweight Cross Section and Panel Spatial Weight Matrix spweightcs Cross Section Spatial Weight Matrix spweightxt Panel Spatial Weight Matrix ------------------------------------------------------------------------------- > -