+-------+ ----+ Title +------------------------------------------------------------
spmstard: (m-STAR) Multiparametric Spatio Temporal AutoRegressive Regression (Spatial Durbin Cross Sections Models)
+-------------------+ ----+ Table of Contents +------------------------------------------------
Syntax Description Options Saved Results References
*** Examples
Authors
+--------+ ----+ Syntax +-----------------------------------------------------------
spmstard depvar indepvars [weight] , wmfile(weight_file) nwmat(#) noconstant aux(varlist) [ stand inv inv2 dist(norm|weib) mfx(lin, log) tolog nolog robust predict(new_var) resid(new_var) iter(#) tech(name) coll zero ll(real 0) level(#) vce(vcetype) maximize other maximization options ]
+-------------+ ----+ Description +------------------------------------------------------
spmstard estimates Spatial econometric regression (MSTAR) "Multiparametric Spatio Temporal AutoRegressive Regression" for Spatial Durbin Cross Sections models.
spmstard estimates Continuous and Truncated Dependent Variables models tobit.
spmstard deals with data either continuous or truncated dependent variable. If depvar has missing values or lower limits, so in this case spmstard will fit spatial cross section model via tobit model, and thus spmstard 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.
spmstard can generate: - Binary / Standardized Weight Matrix. - Inverse / Inverse Squared Standardized Weight Matrix. - Binary / Standardized / Inverse Eigenvalues Variable.
spmstard 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).
+---------+ ----+ 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
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)
spmstard 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
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(norm, exp, weib) can be used.
dist(norm) is the default distribution.
aux(varlist) add Auxiliary Variables into regression model without converting them to spatial lagged variables, i.e., dummy variables. This option dont include these auxiliary variables among spatial lagged variables, it is useful in (spmstard). to avoid lost degrees of freedom (DF). Using many dummy variables must be used with caution to avoid multicollinearity problem, that causes singular matrix, and lead to abort estimation.
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 +----------------------------------------------------
spmstard saves the following results in e():
Scalars
*** Model Selection Diagnostic Criteria: 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(mfx) Beta, Total, Direct, and InDirect Marginal Effect e(mfxe) Beta, Total, Direct, and InDirect Elasticity
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 spmstard. -------------------------------------------------------------------------------
clear all
sysuse spmstard.dta, clear
* (m-STAR) Multiparametric Spatio Temporal AutoRegressive Regression * (m-STAR) Durbin Model
*** YOU MUST HAVE DIFFERENT Weighted Matrixes Files:
* (1) *** Normal Distribution spmstard y x1 x2 , wmfile(SPWmcs1) nwmat(1) dist(norm) spmstard y x1 x2 , wmfile(SPWmcs2) nwmat(2) dist(norm) spmstard y x1 x2 , wmfile(SPWmcs3) nwmat(3) dist(norm) spmstard y x1 x2 , wmfile(SPWmcs4) nwmat(4) dist(norm)
spmstard y x1 x2 , wmfile(SPWmcs4) nwmat(4) dist(norm) aux(x3 x4) spmstard ys x1 x2, wmfile(SPWmcs4) nwmat(4) dist(norm) ll(0) -------------------------------------------------------------------------------
* (2) *** Weibull Distribution spmstard y x1 x2 , wmfile(SPWmcs1) nwmat(1) dist(weib) spmstard y x1 x2 , wmfile(SPWmcs2) nwmat(2) dist(weib) spmstard y x1 x2 , wmfile(SPWmcs3) nwmat(3) dist(weib) spmstard y x1 x2 , wmfile(SPWmcs4) nwmat(4) dist(weib)
spmstard y x1 x2 , wmfile(SPWmcs4) nwmat(4) dist(weib) aux(x3 x4)
spmstard ys x1 x2, wmfile(SPWmcs4) nwmat(4) dist(weib) ll(0) -------------------------------------------------------------------------------
* (3) Weighted mSTAR Normal Distribution: spmstard y x1 x2 [pweight = x1], wmfile(SPWmcs1) nwmat(1) dist(norm) spmstard y x1 x2 [aweight = x1], wmfile(SPWmcs1) nwmat(1) dist(norm) spmstard y x1 x2 [iweight = x1], wmfile(SPWmcs1) nwmat(1) dist(norm) -------------------------------------------------------------------------------
* (4) Weighted mSTAR Weibull Distribution: spmstard y x1 x2 [pweight = x1], wmfile(SPWmcs1) nwmat(1) dist(weib) spmstard y x1 x2 [aweight = x1], wmfile(SPWmcs1) nwmat(1) dist(weib) spmstard y x1 x2 [iweight = x1], wmfile(SPWmcs1) nwmat(1) dist(weib) -------------------------------------------------------------------------------
. clear all . sysuse spmstard.dta, clear . spmstard y x1 x2 , wmfile(SPWmcs1) nwmat(1) dist(norm) mfx(lin) stand
============================================================================== *** Standardized Weight Matrix: 49x49 (Normalized) ==============================================================================
initial: log likelihood = -184.03767 rescale: log likelihood = -184.03767 rescale eq: log likelihood = -184.03767 Iteration 0: log likelihood = -184.03767 Iteration 1: log likelihood = -183.30294 Iteration 2: log likelihood = -183.2614 Iteration 3: log likelihood = -183.26127 Iteration 4: log likelihood = -183.26127 ============================================================================== * MLE Multiparametric Spatio Temporal AutoRegressive Regression * (m-STAR) Spatial Durbin Normal Model (1 Weight Matrix) ============================================================================== y = x1 + x2 + w1x_x1 + w1x_x2 ------------------------------------------------------------------------------ Sample Size = 49 Wald Test = 71.5437 | P-Value > Chi2(4) = 0.0000 F-Test = 17.8859 | P-Value > F(4 , 45) = 0.0000 (Buse 1973) R2 = 0.6192 | Raw Moments R2 = 0.9308 (Buse 1973) R2 Adj = 0.5938 | Raw Moments R2 Adj = 0.9261 Root MSE (Sigma) = 10.6639 | Log Likelihood Function = -183.2613 ------------------------------------------------------------------------------ - R2h= 0.6194 R2h Adj= 0.5940 F-Test = 17.90 P-Value > F(4 , 45) 0.0000 - R2v= 0.6016 R2v Adj= 0.5750 F-Test = 16.61 P-Value > F(4 , 45) 0.0000 ------------------------------------------------------------------------------ - Sum of Rho's = 0.2162738 Sum must be < 1 for Stability Condition ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y | x1 | -.2601291 .0923128 -2.82 0.005 -.4410589 -.0791993 x2 | -1.505436 .3025789 -4.98 0.000 -2.09848 -.9123926 w1x_x1 | -.3976753 .2384109 -1.67 0.095 -.8649521 .0696015 w1x_x2 | .6061678 .6380782 0.95 0.342 -.6444424 1.856778 _cons | 65.24606 17.63594 3.70 0.000 30.68025 99.81187 -------------+---------------------------------------------------------------- Rho1 | .2162738 .1862329 1.16 0.246 -.148736 .5812836 Sigma | 10.13206 1.028118 9.85 0.000 8.116982 12.14713 ------------------------------------------------------------------------------ Wald Test [Rho1=0]: 1.3486 P-Value > Chi2(1) 0.2455 Acceptable Range for Rho1: -1.5345 < Rho1 < 1.0000 ------------------------------------------------------------------------------
* Beta, Total, Direct, and InDirect Linear: Marginal Effect *
+--------------------------------------------------------------------------+ | Variable | Beta(B) | Total | Direct | InDirect | Mean | |--------------+-----------+-----------+-----------+-----------+-----------| |y | | | | | | | x1 | -0.2601 | -0.2573 | -0.2039 | -0.0534 | 38.4362 | | x2 | -1.5054 | -1.4888 | -1.1798 | -0.3090 | 14.3749 | | w1x_x1 | -0.3977 | -0.3933 | -0.3117 | -0.0816 | 37.2777 | | w1x_x2 | 0.6062 | 0.5995 | 0.4751 | 0.1244 | 14.0388 | +--------------------------------------------------------------------------+
* Beta, Total, Direct, and InDirect Linear: Elasticity *
+--------------------------------------------------------------------------+ | Variable | Beta(Es) | Total | Direct | InDirect | Mean | |--------------+-----------+-----------+-----------+-----------+-----------| | x1 | -0.2846 | -0.2815 | -0.2231 | -0.0584 | 38.4362 | | x2 | -0.6160 | -0.6092 | -0.4828 | -0.1264 | 14.3749 | | w1x_x1 | -0.4220 | -0.4173 | -0.3307 | -0.0866 | 37.2777 | | w1x_x2 | 0.2422 | 0.2396 | 0.1899 | 0.0497 | 14.0388 | +--------------------------------------------------------------------------+ Mean of Dependent Variable = 35.1288
+---------+ ----+ Authors +----------------------------------------------------------
- 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
- Sahra Khaleel A. Mickaiel Professor (PhD Economics) Cairo University - Faculty of Agriculture - Department of Economics - Egypt Email: sahra_atta@hotmail.com WebPage: http://sahraecon.110mb.com/stata.htm WebPage at IDEAS: http://ideas.repec.org/f/pmi520.html WebPage at EconPapers: http://econpapers.repec.org/RAS/pmi520.htm
+-------------------+ ----+ spmstard Citation +------------------------------------------------
Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2012) SPMSTARD: "(m-STAR) Spatial Multiparametric Spatio Temporal AutoRegressive Regression: Spatial Durbin Cross Sections Models"
http://ideas.repec.org/c/boc/bocode/s457504.html
http://econpapers.repec.org/software/bocbocode/s457504.htm
Online Help:
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(3) 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