+-------+ ----+ Title +------------------------------------------------------------
r2sem: Overall SEM R2 - Adjusted R2 - F Test - Chi2 Test
+--------+ ----+ Syntax +-----------------------------------------------------------
r2sem
+-------------+ ----+ Description +------------------------------------------------------
r2sem computes overall system R-squared (R2), Adjusted R2, and the overall significance of F-Test, and Chi2-Test, after: - (SEM) Structural Equation Modeling sem for systems of simultaneous equations.
r2sem used Four types of criteria and tests, as discussed in: McElroy(1977), Judge et al(1985), 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) 4- Greene System R2 = 1-(Q/trace(inv(Sig))*SYs)
From each type of these system R2's, r2sem 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|
+---------------+ ----+ Saved Results +----------------------------------------------------
r2sem 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_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_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_g) Greene F Test r(chi_b) Berndt Chi2 Test r(chi_j) Judge Chi2 Test r(chi_m) McElroy Chi2 Test r(chi_g) Greene Chi2 Test r(lsig2) Log Determinant of Sigma r(llf) Log Likelihood Function
+----------+ ----+ Examples +---------------------------------------------------------
in this example FIML will be used as follows:
clear all
sysuse r2sem.dta , clear
sem (y1 <- y2 x1 x2) (y2 <- y1 x3 x4), cov(e.y1*e.y2)
r2sem
return list
* If you want to use dialog box: Press OK to compute r2sem
db r2sem
. sysuse r2sem.dta , clear . sem (y1 <- y2 x1 x2) (y2 <- y1 x3 x4), cov(e.y1*e.y2)
Structural equation model Number of obs = 17 Estimation method = ml Log likelihood = -363.34588 ------------------------------------------------------------------------------ | OIM | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Structural | y1 <- | y2 | .2425937 .2106232 1.15 0.249 -.1702201 .6554075 x1 | .2568409 .462485 0.56 0.579 -.649613 1.163295 x2 | -1.037016 .3154059 -3.29 0.001 -1.6552 -.4188317 _cons | 147.0826 54.4491 2.70 0.007 40.36431 253.8009 -----------+---------------------------------------------------------------- y2 <- | y1 | -.6282929 .6148239 -1.02 0.307 -1.833326 .5767398 x3 | -.5226661 .3235637 -1.62 0.106 -1.156839 .1115071 x4 | 3.4208 1.440664 2.37 0.018 .5971513 6.244449 _cons | 62.44495 42.36071 1.47 0.140 -20.58052 145.4704 -------------+---------------------------------------------------------------- Variance | e.y1 | 80.17577 28.99122 39.46865 162.8673 e.y2 | 142.4478 80.80501 46.86006 433.0208 -------------+---------------------------------------------------------------- Covariance | e.y1 | e.y2 | 25.62619 53.75243 0.48 0.634 -79.72665 130.979 ------------------------------------------------------------------------------ LR test of model vs. saturated: chi2(2) = 0.12, Prob > chi2 = 0.9408
. r2sem ============================================================================== * Structural Equation Modeling: SEM - Method(ml) * Overall System R2 - Adjusted R2 - F-Test - Chi2-Test ==============================================================================
+----------------------------------------------------------------------------+ | Name | R2 | Adj_R2 | F | P-Value | Chi2 | P-Value | |----------+----------+----------+----------+----------+----------+----------| | Berndt | 0.9189 | 0.8962 | 40.4497 | 0.0000 | 42.6990 | 0.0000 | | McElroy | 0.8043 | 0.7495 | 14.6785 | 0.0000 | 27.7303 | 0.0002 | | Judge | 0.8227 | 0.7731 | 16.5746 | 0.0000 | 29.4107 | 0.0001 | | Greene | 0.8096 | 0.7563 | 15.1863 | 0.0000 | 28.1969 | 0.0002 | +----------------------------------------------------------------------------+ Number of Parameters = 9 Number of Equations = 2 Degrees of Freedom F-Test = (7, 34) Degrees of Freedom Chi2-Test = 7 Log Determinant of Sigma = 9.2840 Log Likelihood Function = -363.3459
+------------+ ----+ References +-------------------------------------------------------
Berndt, Ernst R. (1991) "The practice of econometrics: Classical and contemporary", Addison-Wesley Publishing Company; 468.
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.
+--------+ ----+ 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
+----------------+ ----+ r2sem Citation +---------------------------------------------------
Shehata, Emad Abd Elmessih (2012) R2SEM: "Stata Module to Compute Overall R2, Adj. R2, F-Test, and Chi2-Test after Structural Equation Modeling (SEM) Regressions"
Online Help:
lmasem, lmhsem, lmnsem, lmcovsem, r2sem, lmareg3, lmhreg3, lmnreg3, lmcovreg3, r2reg3. (if installed).