help: r2sem dialog:

Title

r2sem: (SEM-FIML) Overall System R2 - Adjusted R2 - F Test - Chi2 Test

Table of Contents

Syntax

Description

Saved Results

References

*** Examples

Author

Syntax

r2sem

Description

r2sem computes Overall System R-squared (R2), Adjusted R2, and the overall significance of F-Test, and Chi2-Test, after:

- sem: (SEM) Structural Equation Modeling for systems of simultaneous equations.

r2sem used 4 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 (NxQ)
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 LLF

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.

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

. clear all
. sysuse r2sem.dta , clear
. sem (y1 <- y2 x1 x2) (y2 <- y1 x3 x4), cov(e.y1*e.y2)

Endogenous variables

Observed: y1 y2

Exogenous variables

Observed: x1 x2 x3 x4

Fitting target model:

Iteration 0: log likelihood = -363.34854
Iteration 1: log likelihood = -363.34588
Iteration 2: log likelihood = -363.34588

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)
* (SEM-FIML) 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
------------------------------------------------------------------------------

Author

- Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
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 (SEM-FIML) Overall System R2 - Adjusted R2 - F Test - Chi2 Test"

http://ideas.repec.org/c/boc/bocode/s457431.html

http://econpapers.repec.org/software/bocbocode/s457431.htm

Online Help:

* (1) (3SLS-SUR) * Simultaneous Equations:
lmareg3 (3SLS-SUR) Overall System Autocorrelation Tests
lmhreg3 (3SLS-SUR) Overall System Heteroscedasticity Tests
lmnreg3 (3SLS-SUR) Overall System Non Normality Tests
lmcovreg3 (3SLS-SUR) Breusch-Pagan Diagonal Covariance Matrix
r2reg3 (3SLS-SUR) Overall System R2, F-Test, and Chi2-Test
diagreg3 (3SLS-SUR) Overall System Model Selection Diagnostic Criteria
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* (2) (SEM-FIML) * Structural Equation Modeling:
lmasem (SEM-FIML) Overall System Autocorrelation Tests
lmhsem (SEM-FIML) Overall System Heteroscedasticity Tests
lmnsem (SEM-FIML) Overall System Non Normality Tests
lmcovsem (SEM-FIML) Breusch-Pagan Diagonal Covariance Matrix Test
r2sem (SEM-FIML) Overall System R2, F-Test, and Chi2-Test
diagsem (SEM-FIML) Overall System Model Selection Diagnostic Criteria
---------------------------------------------------------------------------
* (3) (NL-SUR) * Non Linear Seemingly Unrelated Regression:
lmanlsur (NL-SUR) Overall System Autocorrelation Tests
lmhnlsur (NL-SUR) Overall System Heteroscedasticity Tests
lmnnlsur (NL-SUR) Overall System Non Normality Tests
lmcovnlsur (NL-SUR) Breusch-Pagan Diagonal Covariance Matrix Test
r2nlsur (NL-SUR) Overall System R2, F-Test, and Chi2-Test
diagnlsur (NL-SUR) Overall System Model Selection Diagnostic Criteria
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* (4) (VAR) * Vector Autoregressive Model:
lmavar (VAR) Overall System Autocorrelation Tests
lmhvar (VAR) Overall System Heteroscedasticity Tests
lmnvar (VAR) Overall System Non Normality Tests
lmcovvar (VAR) Breusch-Pagan Diagonal Covariance Matrix Test
r2var (VAR) Overall System R2, F-Test, and Chi2-Test
diagvar (VAR) Overall System Model Selection Diagnostic Criteria
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