+-------+ ----+ Title +------------------------------------------------------------
r2nlsur: Overall NL-SUR System R2 - Adjusted R2 - F Test - Chi2 Test
+--------+ ----+ Syntax +-----------------------------------------------------------
r2nlsur
+-------------+ ----+ Description +------------------------------------------------------
r2nlsur computes Overall Nonlinear Seemingly Unrelated Regression (NL-SUR) System R2, Adj. R2, F-Test, and Chi2-Test after: - (NL-SUR) Nonlinear Seemingly Unrelated Regression nlsur for sets of equations.
r2nlsur used Four types of criteria and tests, as discussed in: McElroy(1977), Judge et al(1985), Dhrymes(1974), Greene(1993), and Berndt(1991). see eq.12.1.33-36 in Judge et al(1985, p.477).
1- Berndt System R2 = 1-|E'E| / |Yb'Yb| 2- McElroy System R2 = 1-(U'W*U)/ (Y'W*Y) 3- Judge System R2 = 1-(U'U) / (Y'Y) Q 4- Dhrymes System R2 = Sum [R2i (yi' Dt yi']/[Y(I(Q) # Dt)Y] i=1 5- Greene System R2 = 1-(Q/trace(inv(Sig))*SYs)
Judge and Dhrymes are identical results.
From each type of these system R2's, r2nlsur can calculate Adjusted R2, F-Test, and Chi2-Test:
Adjusted R2 = 1-(1-R2)*((QN-Q)/(QN-K)) F-Test = R2/(1-R2)*[(QN-K)/(K-Q)] Chi2-Test = -N*(log(1-R2))
where |E'E| = determinant of residual matrix (NxQ) |Yb'Yb| = determinant of dependent variables matrix in deviation from mean (Nx > Q) yi = dependent variable of eq. i (Nx1) Y = stacked vector of dependent variables (QNx1) U = stacked vector of residuals (QNx1) W = variance-covariance matrix of residuals (W=inv(Omega) # I(N)) N = number of observations K = Number of Parameters Q = Number of Equations R2i = R2 of eq. i Dt = I(N)-JJ'/N, with J=(1,1,...,1)' (Nx1) SYs = (Yb1*Yb2*...Ybq)/N Sig = Sigma hat Matrix Degrees of Freedom F-Test = (K-Q), (QN) Degrees of Freedom Chi2-Test = (K-Q) Log Determinant of Sigma = log|Sigma matrix| Log Likelihood Function LLF =-(N*Q/2)*(1+log(2*_pi))-(N/2*abs(log(Sigma)))
+---------------+ ----+ Saved Results +----------------------------------------------------
r2nlsur saves the following in r():
Scalars r(N) Number of Observations r(k) Number of Parameters r(k_eq) Number of Equations r(chi_df) DF chi-squared r(f_df1) F-Test DF1 Numerator r(f_df2) F-Test DF2 Denominator r(r2_b) Berndt R-squared r(r2_j) Judge R-squared r(r2_m) McElroy R-squared r(r2_d) Dhrymes R-squared r(r2_g) Greene R-squared r(r2a_b) Berndt Adjusted R-squared r(r2a_j) Judge Adjusted R-squared r(r2a_m) McElroy Adjusted R-squared r(r2a_d) Dhrymes Adjusted R-squared r(r2a_g) Greene Adjusted R-squared r(f_b) Berndt F Test r(f_j) Judge F Test r(f_m) McElroy F Test r(f_d) Dhrymes F Test r(f_g) Greene F Test r(chi_b) Berndt Chi2 Test r(chi_j) Judge Chi2 Test r(chi_m) McElroy Chi2 Test r(chi_d) Dhrymes Chi2 Test r(chi_g) Greene Chi2 Test r(lsig2) Log Determinant of Sigma r(llf) Log Likelihood Function
+------------+ ----+ References +-------------------------------------------------------
Berndt, Ernst R. (1991) "The practice of econometrics: Classical and contemporary", Addison-Wesley Publishing Company; 468.
Dhrymes, Phoebus J. (1974) "Econometrics: Statistical Foundations and Applications", 2ed edition Springer- Verlag New York, USA..
Greene, William (1993) "Econometric Analysis", 2nd ed., Macmillan Publishing Company Inc., New York, USA.; 490-491.
Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, & Tsoung-Chao Lee(1985) "The Theory and Practice of Econometrics", 2nd ed., John Wiley & Sons, Inc., New York, USA; 477-478.
Kmenta, Jan (1986) "Elements of Econometrics", 2nd ed., Macmillan Publishing Company, Inc., New York, USA; 645.
McElroy, Marjorie B. (1977) "Goodness of Fit for Seemingly Unrelated Regressions: Glahn's R2y,x and Hooper's r~2", Journal of Econometrics, 6(3), November; 381-387.
+----------+ ----+ Examples +---------------------------------------------------------
clear all
sysuse r2nlsur.dta , clear
nlsur (y1={B10}+{B11}*y2+{B12}*x1+{B13}*x2) (y2={B20}+{B21}*y1+{B22}*x3+{B23}* > x4) r2nlsur
sureg (y1 y2 x1 x2) (y2 y1 x3 x4) r2reg3
return list
* If you want to use dialog box: Press OK to compute r2nlsur
db r2nlsur
. sysuse r2nlsur.dta , clear . nlsur (y1 = {B10} + {B11}*x1+ {B12}*x2) (y2 = {B20} + {B21}*x3+ {B22}*x4)
FGNLS regression --------------------------------------------------------------------- Equation | Obs Parms RMSE R-sq Constant ----------------+---------------------------------------------------- 1 y1 | 17 3 9.056705 0.8555 B10 2 y2 | 17 3 10.75922 0.8318 B20 ---------------------------------------------------------------------
------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /B10 | 183.5815 43.95101 4.18 0.000 97.43906 269.7239 /B11 | .4956588 .4326135 1.15 0.252 -.352248 1.343566 /B12 | -1.370874 .1363473 -10.05 0.000 -1.63811 -1.103638 /B20 | 37.62409 30.21636 1.25 0.213 -21.59888 96.84706 /B21 | -.3675841 .2675172 -1.37 0.169 -.8919083 .15674 /B22 | 2.288538 .8959307 2.55 0.011 .5325456 4.04453 ------------------------------------------------------------------------------
. r2nlsur ============================================================================== * Overall NL-SUR System R2 - Adjusted R2 - F Test - Chi2 Test (fgnls) ==============================================================================
+----------------------------------------------------------------------------+ | Name | R2 | Adj_R2 | F | P-Value | Chi2 | P-Value | |----------+----------+----------+----------+----------+----------+----------| | Berndt | 0.9293 | 0.9192 | 92.0573 | 0.0000 | 45.0464 | 0.0000 | | McElroy | 0.8315 | 0.8074 | 34.5394 | 0.0000 | 30.2724 | 0.0000 | | Judge | 0.8425 | 0.8200 | 37.4452 | 0.0000 | 31.4219 | 0.0000 | | Dhrymes | 0.8425 | 0.8200 | 37.4452 | 0.0000 | 31.4219 | 0.0000 | | Greene | 0.8133 | 0.7866 | 30.4844 | 0.0000 | 28.5263 | 0.0000 | +----------------------------------------------------------------------------+ Number of Parameters = 6 Number of Equations = 2 Degrees of Freedom F-Test = (4, 34) Degrees of Freedom Chi2-Test = 4 Log Determinant of Sigma = 9.1462 Log Likelihood Function = -125.9864 -------------------------------------------------------------------------------
+--------+ ----+ Author +-----------------------------------------------------------
Emad Abd Elmessih Shehata Assistant Professor 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
+------------------+ ----+ r2nlsur Citation +-------------------------------------------------
Shehata, Emad Abd Elmessih (2012) R2NLSUR: "Overall Nonlinear Seemingly Unrelated Regression (NL-SUR) System R2, Adj. R2, F-Test, and Chi2-Test after (nlsur) Regressions"
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