{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}