{smcl}
{hline}
{cmd:help: {helpb r2sem}}{space 50} {cmd:dialog:} {bf:{dialog r2sem}}
{hline}
{bf:{err:{dlgtab:Title}}}
{bf:r2sem: (SEM-FIML) Overall System R2 - Adjusted R2 - F Test - Chi2 Test}
{marker 00}{bf:{err:{dlgtab:Table of Contents}}}
{p 4 8 2}
{p 5}{helpb r2sem##01:Syntax}{p_end}
{p 5}{helpb r2sem##02:Description}{p_end}
{p 5}{helpb r2sem##03:Saved Results}{p_end}
{p 5}{helpb r2sem##04:References}{p_end}
{p 1}*** {helpb r2sem##05:Examples}{p_end}
{p 5}{helpb r2sem##06:Author}{p_end}
{marker 01}{bf:{err:{dlgtab:Syntax}}}
{cmd: r2sem}
{marker 02}{bf:{err:{dlgtab:Description}}}
{p 2 2 2}{cmd:r2sem} computes Overall System R-squared (R2), Adjusted R2, and the overall significance of F-Test, and Chi2-Test, after:{p_end}
{p 3 2 2}- {helpb sem}: (SEM) Structural Equation Modeling for systems of simultaneous equations.{p_end}
{p 2 2 2}{cmd:r2sem} used 4 types of criteria and tests, as discussed in:{p_end}
{p 2 2 2}{cmd: McElroy(1977), Judge et al(1985), Greene(1993), and Berndt(1991)}.{p_end}
{p 6 2 2}see eq.12.1.33-36 in Judge et al(1985, p.477).{p_end}
{cmd:1- Berndt System R2} = 1-|E'E| / |Yb'Yb|
{cmd:2- McElroy System R2} = 1-(U'W*U)/ (Y'W*Y)
{cmd:3- Judge System R2} = 1-(U'U) / (Y'Y)
{cmd:4- Greene System R2} = 1-(Q/trace(inv(Sig))*SYs)
{p 2 2 2}From each type of these system R2's, {cmd:r2sem} can calculate Adjusted R2, F-Test, and Chi2-Test:{p_end}
{cmd:Adjusted R2} = 1-(1-R2)*((QN-Q)/(QN-K))
{cmd:F-Test} = R2/(1-R2)*[(QN-K)/(K-Q)]
{cmd: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|
{marker 03}{bf:{err:{dlgtab:Saved Results}}}
{pstd}
{cmd:r2sem} saves the following in {cmd:r()}:
{synoptset 15 tabbed}{...}
{p2col 5 15 15 2: Scalars}{p_end}
{col 4}{cmd:r(N)}{col 20}Number of Observations
{col 4}{cmd:r(k)}{col 20}Number of Parameters
{col 4}{cmd:r(k_eq)}{col 20}Number of Equations
{col 4}{cmd:r(chi_df)}{col 20}DF chi-squared
{col 4}{cmd:r(f_df1)}{col 20}F-Test DF1 Numerator
{col 4}{cmd:r(f_df2)}{col 20}F-Test DF2 Denominator
{col 4}{cmd:r(r2_b)}{col 20}Berndt R-squared
{col 4}{cmd:r(r2_j)}{col 20}Judge R-squared
{col 4}{cmd:r(r2_m)}{col 20}McElroy R-squared
{col 4}{cmd:r(r2_g)}{col 20}Greene R-squared
{col 4}{cmd:r(r2a_b)}{col 20}Berndt Adjusted R-squared
{col 4}{cmd:r(r2a_j)}{col 20}Judge Adjusted R-squared
{col 4}{cmd:r(r2a_m)}{col 20}McElroy Adjusted R-squared
{col 4}{cmd:r(r2a_g)}{col 20}Greene Adjusted R-squared
{col 4}{cmd:r(f_b)}{col 20}Berndt F Test
{col 4}{cmd:r(f_j)}{col 20}Judge F Test
{col 4}{cmd:r(f_m)}{col 20}McElroy F Test
{col 4}{cmd:r(f_g)}{col 20}Greene F Test
{col 4}{cmd:r(chi_b)}{col 20}Berndt Chi2 Test
{col 4}{cmd:r(chi_j)}{col 20}Judge Chi2 Test
{col 4}{cmd:r(chi_m)}{col 20}McElroy Chi2 Test
{col 4}{cmd:r(chi_g)}{col 20}Greene Chi2 Test
{col 4}{cmd:r(lsig2)}{col 20}Log Determinant of Sigma
{col 4}{cmd:r(llf)}{col 20}Log Likelihood Function{col 62}LLF
{marker 04}{bf:{err:{dlgtab:References}}}
{p 4 8 2}Berndt, Ernst R. (1991)
{cmd: "The practice of econometrics: Classical and contemporary",}
{it:Addison-Wesley Publishing Company}; 468.
{p 4 8 2}Greene, William (1993)
{cmd: "Econometric Analysis",}
{it:2nd ed., Macmillan Publishing Company Inc., New York, USA.}; 490-491.
{p 4 8 2}Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, & Tsoung-Chao Lee(1985)
{cmd: "The Theory and Practice of Econometrics",}
{it:2nd ed., John Wiley & Sons, Inc., New York, USA}; 477-478.
{p 4 8 2}Kmenta, Jan (1986)
{cmd: "Elements of Econometrics",}
{it:2nd ed., Macmillan Publishing Company, Inc., New York, USA}; 645.
{p 4 8 2}McElroy, Marjorie B. (1977)
{cmd: "Goodness of Fit for Seemingly Unrelated Regressions: Glahn's R2y,x and Hooper's r~2",}
{it:Journal of Econometrics, 6(3), November}; 381-387.
{marker 05}{bf:{err:{dlgtab:Examples}}}
in this example FIML will be used as follows:
{stata clear all}
{stata sysuse r2sem.dta , clear}
{stata sem (y1 <- y2 x1 x2) (y2 <- y1 x3 x4), cov(e.y1*e.y2)}
{stata r2sem}
{stata return list}
* If you want to use dialog box: Press OK to compute r2sem
{stata db r2sem}
{hline}
. 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
------------------------------------------------------------------------------
{marker 06}{bf:{err:{dlgtab:Author}}}
- {hi:Emad Abd Elmessih Shehata}
{hi:Professor (PhD Economics)}
{hi:Agricultural Research Center - Agricultural Economics Research Institute - Egypt}
{hi:Email: {browse "mailto:emadstat@hotmail.com":emadstat@hotmail.com}}
{hi:WebPage at IDEAS:{col 27}{browse "http://ideas.repec.org/f/psh494.html"}}
{hi:WebPage at EconPapers:{col 27}{browse "http://econpapers.repec.org/RAS/psh494.htm"}}
{bf:{err:{dlgtab:R2SEM Citation}}}
{p 1}{cmd:Shehata, Emad Abd Elmessih (2012)}{p_end}
{p 1 10 1}{cmd:R2SEM: "Stata Module to Compute (SEM-FIML) Overall System R2 - Adjusted R2 - F Test - Chi2 Test"}{p_end}
{browse "http://ideas.repec.org/c/boc/bocode/s457431.html"}
{browse "http://econpapers.repec.org/software/bocbocode/s457431.htm"}
{title:Online Help:}
{bf:{err:* (1) (3SLS-SUR) * Simultaneous Equations:}}
{helpb lmareg3}{col 12}(3SLS-SUR) Overall System Autocorrelation Tests
{helpb lmhreg3}{col 12}(3SLS-SUR) Overall System Heteroscedasticity Tests
{helpb lmnreg3}{col 12}(3SLS-SUR) Overall System Non Normality Tests
{helpb lmcovreg3}{col 12}(3SLS-SUR) Breusch-Pagan Diagonal Covariance Matrix
{helpb r2reg3}{col 12}(3SLS-SUR) Overall System R2, F-Test, and Chi2-Test
{helpb diagreg3}{col 12}(3SLS-SUR) Overall System Model Selection Diagnostic Criteria
---------------------------------------------------------------------------
{bf:{err:* (2) (SEM-FIML) * Structural Equation Modeling:}}
{helpb lmasem}{col 12}(SEM-FIML) Overall System Autocorrelation Tests
{helpb lmhsem}{col 12}(SEM-FIML) Overall System Heteroscedasticity Tests
{helpb lmnsem}{col 12}(SEM-FIML) Overall System Non Normality Tests
{helpb lmcovsem}{col 12}(SEM-FIML) Breusch-Pagan Diagonal Covariance Matrix Test
{helpb r2sem}{col 12}(SEM-FIML) Overall System R2, F-Test, and Chi2-Test
{helpb diagsem}{col 12}(SEM-FIML) Overall System Model Selection Diagnostic Criteria
---------------------------------------------------------------------------
{bf:{err:* (3) (NL-SUR) * Non Linear Seemingly Unrelated Regression:}}
{helpb lmanlsur}{col 12}(NL-SUR) Overall System Autocorrelation Tests
{helpb lmhnlsur}{col 12}(NL-SUR) Overall System Heteroscedasticity Tests
{helpb lmnnlsur}{col 12}(NL-SUR) Overall System Non Normality Tests
{helpb lmcovnlsur}{col 12}(NL-SUR) Breusch-Pagan Diagonal Covariance Matrix Test
{helpb r2nlsur}{col 12}(NL-SUR) Overall System R2, F-Test, and Chi2-Test
{helpb diagnlsur}{col 12}(NL-SUR) Overall System Model Selection Diagnostic Criteria
---------------------------------------------------------------------------
{bf:{err:* (4) (VAR) * Vector Autoregressive Model:}}
{helpb lmavar}{col 12}(VAR) Overall System Autocorrelation Tests
{helpb lmhvar}{col 12}(VAR) Overall System Heteroscedasticity Tests
{helpb lmnvar}{col 12}(VAR) Overall System Non Normality Tests
{helpb lmcovvar}{col 12}(VAR) Breusch-Pagan Diagonal Covariance Matrix Test
{helpb r2var}{col 12}(VAR) Overall System R2, F-Test, and Chi2-Test
{helpb diagvar}{col 12}(VAR) Overall System Model Selection Diagnostic Criteria
---------------------------------------------------------------------------
{psee}
{p_end}