{smcl} {hline} {cmd:help: {helpb ridge2sls}}{space 50} {cmd:dialog:} {bf:{dialog ridge2sls}} {hline} {bf:{err:{dlgtab:Title}}} {bf: ridge2sls: Two-Stage Least Squares (2SLS): Ridge & Weighted Regression} {marker 00}{bf:{err:{dlgtab:Table of Contents}}} {p 4 8 2} {p 5}{helpb ridge2sls##01:Syntax}{p_end} {p 5}{helpb ridge2sls##02:Description}{p_end} {p 5}{helpb ridge2sls##03:Ridge Options}{p_end} {p 5}{helpb ridge2sls##04:Weight Options}{p_end} {p 5}{helpb ridge2sls##05:Weighted Variable Type Options}{p_end} {p 5}{helpb ridge2sls##06:Options}{p_end} {p 5}{helpb ridge2sls##07:Model Selection Diagnostic Criteria}{p_end} {p 5}{helpb ridge2sls##08:Saved Results}{p_end} {p 5}{helpb ridge2sls##09:References}{p_end} {p 1}*** {helpb ridge2sls##10:Examples}{p_end} {p 5}{helpb ridge2sls##11:Authors}{p_end} {marker 01}{bf:{err:{dlgtab:Syntax}}} {p 2 4 2} {cmd:ridge2sls} {depvar} {it:{help varlist:indepvars}} {cmd:({it:{help varlist:endog}} = {it:{help varlist:inst}})} {ifin} , {p_end} {p 6 6 2} {err: [} {opt rid:ge(orr|grr1|grr2|grr3)} {opt kr(#)} {opt dn diag}{p_end} {p 8 6 2} {opt mfx(lin|log)} {opt weights(yh|yh2|abse|e2|le2|x|xi|x2|xi2)} {opt wv:ar(varname)}{p_end} {p 8 6 2} {opt first} {opt nocons:tant} {opt noconexog} {opt pred:ict(new_var)} {opt res:id(new_var)} {err:]}{p_end} {marker 02}{bf:{err:{dlgtab:Description}}} {pstd} {cmd:ridge2sls} estimates Two-Stage Least Squares (2SLS), with Ridge and Weighted Regression, and computes Model Selection Diagnostic Criteria, and Marginal Effects and Elasticities. {p 3 4 2} R2, R2 Adjusted, and F-Test, are obtained from 3 ways:{p_end} {p 5 4 2} 1- (Buse 1973) R2.{p_end} {p 5 4 2} 2- Raw Moments R2.{p_end} {p 5 4 2} 3- Corrected R2, if original R2 is negative.{p_end} {p 5 4 2} - Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1).{p_end} {p 5 4 2} - F-Test=R2/(1-R2)*(N-K-1)/(K).{p_end} {p 5 4 2} - Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1).{p_end} {marker 03}{bf:{err:{dlgtab:Ridge Options}}} {p 3 6 2} {opt kr(#)} Ridge k value, must be in the range (0 < k < 1).{p_end} {p 3 6 2}IF {bf:kr(0)} in {opt ridge(orr, grr1, grr2, grr3)}, the model will be an IV-2SLS regression.{p_end} {col 3}{bf:ridge({err:{it:orr}})} : Ordinary Ridge Regression [Judge,et al(1988,p.878) eq.21.4.2]. {col 3}{bf:ridge({err:{it:grr1}})}: Generalized Ridge Regression [Judge,et al(1988,p.881) eq.21.4.12]. {col 3}{bf:ridge({err:{it:grr2}})}: Iterative Generalized Ridge [Judge,et al(1988,p.881) eq.21.4.12]. {col 3}{bf:ridge({err:{it:grr3}})}: Adaptive Generalized Ridge [Strawderman(1978)]. {p 2 4 2}{cmd:ridge2sls} estimates Ordinary Ridge regression as a multicollinearity remediation method.{p_end} {p 2 4 2}General form of Ridge Coefficients and Covariance Matrix are:{p_end} {p 2 4 2}{cmd:Br = inv[X'X + kI] X'Y}{p_end} {p 2 4 2}{cmd:Cov=Sig^2 * inv[X'X + kI] (X'X) inv[X'X + kI]}{p_end} where: Br = Ridge Coefficients Vector (k x 1). Cov = Ridge Covariance Matrix (k x k). Y = Dependent Variable Vector (N x 1). X = Independent Variables Matrix (N x k). k = Ridge Value (0 < k < 1). I = Diagonal Matrix of Cross Product Matrix (Xs'Xs). Xs = Standardized Variables Matrix in Deviation from Mean. Sig2 = (Y-X*Br)'(Y-X*Br)/DF {marker 04}{bf:{err:{dlgtab:Weight Options}}} {synoptset 16}{...} {synopt:{bf:wvar({err:{it:varname}})}}Weighted Variable Name{p_end} {marker 05}{bf:{err:{dlgtab:Weighted Variable Type Options}}} {synoptset 16}{...} {p2coldent:{it:Type Options}}Description{p_end} {synopt:{bf:weights({err:{it:yh}})}}Yh - Predicted Value{p_end} {synopt:{bf:weights({err:{it:yh2}})}}Yh^2 - Predicted Value Squared{p_end} {synopt:{bf:weights({err:{it:abse}})}}abs(E) - Absolute Value of Residual{p_end} {synopt:{bf:weights({err:{it:e2}})}}E^2 - Residual Squared{p_end} {synopt:{bf:weights({err:{it:le2}})}}log(E^2) - Log Residual Squared{p_end} {synopt:{bf:weights({err:{it:x}})}}(x) Variable{p_end} {synopt:{bf:weights({err:{it:xi}})}}(1/x) Inverse Variable{p_end} {synopt:{bf:weights({err:{it:x2}})}}(x^2) Squared Variable{p_end} {synopt:{bf:weights({err:{it:xi2}})}}(1/x^2) Inverse Squared Variable{p_end} {marker 06}{bf:{err:{dlgtab:Options}}} {synoptset 16}{...} {col 3}{opt dn}{col 20}Use (N) divisor instead of (N-K) for Degrees of Freedom (DF) {col 3}{opt first}{col 20}Display Reduced Form Equations (First Stage Regression {col 3}{opt nocons:tant}{col 20}Exclude Constant Term from RHS Equation only {col 3}{bf:noconexog}{col 20}Exclude Constant Term from all Equations {col 20}(both RHS and Instrumental Equations). {col 20}Results of using {cmd:noconexog} option are identical to {col 20}Stata {helpb ivregress}. {col 20}Including Constant Term in both RHS and Instrumental Equations {col 20}is default in {cmd:ridge2sls} {col 3}{opt mfx(lin, log)}{col 20}functional form: Linear model {cmd:(lin)}, or Log-Log model {cmd:(log)}, {col 20}to compute Marginal Effects and Elasticities - In Linear model: marginal effects are the coefficients (Bm), and elasticities are (Es = Bm X/Y). - In Log-Log model: elasticities are the coefficients (Es), and the marginal effects are (Bm = Es Y/X). {synopt:{opt pred:ict(new_var)}}Predicted values variable{p_end} {synopt:{opt res:id(new_var)}}Residuals values variable{p_end} {p2colreset}{...} {marker 07}{bf:{err:{dlgtab:Model Selection Diagnostic Criteria}}} {synopt:{opt diag}}Model Selection Diagnostic Criteria{p_end} - Log Likelihood Function LLF - Akaike Information Criterion (1974) AIC - Akaike Information Criterion (1973) Log AIC - Schwarz Criterion (1978) SC - Schwarz Criterion (1978) Log SC - Amemiya Prediction Criterion (1969) FPE - Hannan-Quinn Criterion (1979) HQ - Rice Criterion (1984) Rice - Shibata Criterion (1981) Shibata - Craven-Wahba Generalized Cross Validation (1979) GCV {marker 08}{bf:{err:{dlgtab:Saved Results}}} {pstd} {cmd:ridge2sls} saves the following in {cmd:e()}: {err:*** Model Selection Diagnostic Criteria:} {col 4}{cmd:e(N)}{col 20}number of observations {col 4}{cmd:e(r2bu)}{col 20}R-squared (Buse 1973) {col 4}{cmd:e(r2bu_a)}{col 20}R-squared Adj (Buse 1973) {col 4}{cmd:e(r2raw)}{col 20}Raw Moments R2 {col 4}{cmd:e(r2raw_a)}{col 20}Raw Moments R2 Adj {col 4}{cmd:e(f)}{col 20}F-test {col 4}{cmd:e(fp)}{col 20}F-test P-Value {col 4}{cmd:e(wald)}{col 20}Wald-test {col 4}{cmd:e(waldp)}{col 20}Wald-test P-Value {col 4}{cmd:e(r2cc)}{col 20}Corrected R2 {col 4}{cmd:e(r2cc_a)}{col 20}adj Corrected R2 {col 4}{cmd:e(sig)}{col 20}Sigma (MSE) {col 4}{cmd:e(llf)}{col 20}Log Likelihood Function{col 62}LLF {col 4}{cmd:e(aic)}{col 20}Akaike Information Criterion{col 62}(1974) AIC {col 4}{cmd:e(laic)}{col 20}Akaike Information Criterion{col 62}(1973) Log AIC {col 4}{cmd:e(sc)}{col 20}Schwarz Criterion{col 62}(1978) SC {col 4}{cmd:e(lsc)}{col 20}Schwarz Criterion{col 62}(1978) Log SC {col 4}{cmd:e(fpe)}{col 20}Amemiya Prediction Criterion{col 62}(1969) FPE {col 4}{cmd:e(hq)}{col 20}Hannan-Quinn Criterion{col 62}(1979) HQ {col 4}{cmd:e(rice)}{col 20}Rice Criterion{col 62}(1984) Rice {col 4}{cmd:e(shibata)}{col 20}Shibata Criterion{col 62}(1981) Shibata {col 4}{cmd:e(gcv)}{col 20}Craven-Wahba Generalized Cross Validation (1979) GCV Matrixes {col 4}{cmd:e(b)}{col 20}coefficient vector {col 4}{cmd:e(V)}{col 20}variance-covariance matrix of the estimators {col 4}{cmd:e(mfxlin)}{col 20}Marginal Effect and Elasticity in Lin Form {col 4}{cmd:e(mfxlog)}{col 20}Marginal Effect and Elasticity in Log Form {marker 09}{bf:{err:{dlgtab:References}}} {p 4 8 2}Damodar Gujarati (1995) {cmd: "Basic Econometrics"} {it:3rd Edition, McGraw Hill, New York, USA}. {p 4 8 2}Evagelia, Mitsaki (2011) {cmd: "Ridge Regression Analysis of Collinear Data",} {browse "http://www.stat-athens.aueb.gr/~jpan/diatrives/Mitsaki/chapter2.pdf"} {p 4 8 2}Greene, William (2007) {cmd: "Econometric Analysis",} {it:6th ed., Upper Saddle River, NJ: Prentice-Hall}; 387-388. {p 4 8 2}Griffiths, W., R. Carter Hill & George Judge (1993) {cmd: "Learning and Practicing Econometrics",} {it:John Wiley & Sons, Inc., New York, USA}; 602-606. {p 4 8 2}Hoerl A. E. (1962) {cmd: "Application of Ridge Analysis to Regression Problems",} {it:Chemical Engineering Progress, 58}; 54-59. {p 4 8 2}Hoerl, A. E. and R. W. Kennard (1970a) {cmd: "Ridge Regression: Biased Estimation for Non-Orthogonal Problems",} {it:Technometrics, 12}; 55-67. {p 4 8 2}Hoerl, A. E. and R. W. Kennard (1970b) {cmd: "Ridge Regression: Applications to Non-Orthogonal Problems",} {it:Technometrics, 12}; 69-82. {p 4 8 2}Hoerl, A. E. ,R. W. Kennard, & K. Baldwin (1975) {cmd: "Ridge Regression: Some Simulations",} {it:Communications in Statistics, A, 4}; 105-123. {p 4 8 2}Hoerl, A. E. and R. W. Kennard (1976) {cmd: "Ridge Regression: Iterative Estimation of the Biasing Parameter",} {it:Communications in Statistics, A, 5}; 77-88. {p 4 8 2}Judge, Georege, R. Carter Hill, William . E. Griffiths, Helmut Lutkepohl, & Tsoung-Chao Lee (1988) {cmd: "Introduction To The Theory And Practice Of Econometrics",} {it:2nd ed., John Wiley & Sons, Inc., New York, USA}. {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}; 615. {p 4 8 2}Kmenta, Jan (1986) {cmd: "Elements of Econometrics",} {it: 2nd ed., Macmillan Publishing Company, Inc., New York, USA}; 718. {p 4 8 2}Marquardt D.W. (1970) {cmd: "Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation",} {it:Technometrics, 12}; 591-612. {p 4 8 2}Marquardt D.W. & R. Snee (1975) {cmd: "Ridge Regression in Practice",} {it:The American Statistician, 29}; 3-19. {p 4 8 2}Theil, Henri (1971) {cmd: "Principles of Econometrics",} {it:John Wiley & Sons, Inc., New York, USA}. {p 4 8 2}White, Halbert (1980) {cmd: "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity",} {it:Econometrica, 48}; 817-838. {p 4 8 2}William E. Griffiths, R. Carter Hill and George G. Judge (1993) {cmd: "Learning and Practicing Econometrics",} {it:John Wiley & Sons, Inc., New York, USA}. {marker 10}{bf:{err:{dlgtab:Examples}}} {stata clear all} {stata sysuse ridge2sls.dta , clear} {stata db ridge2sls} {bf:{err:* (1) Two Stages Least Squares (2SLS)}} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(grr1) diag mfx(lin)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , mfx(log)} {hline} {bf:{err:* (2) Weighted Two Stages Least Squares (W2SLS)}} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(yh)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(yh2)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(abse)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(e2)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(le2)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(x) wvar(x1)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(xi) wvar(x1)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(x2) wvar(x1)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , weights(xi2) wvar(x1)} {hline} {bf:{err:* (3) Ridge Two Stages Least Squares (R2SLS)}} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(orr) kr(0.5) weights(x) wvar(x1)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(orr) kr(0.5)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(grr1)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(grr2)} {stata ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(grr3)} {hline} . clear all . sysuse ridge2sls.dta , clear . ridge2sls y1 x1 x2 (y2 = x1 x2 x3 x4) , ridge(grr1) diag mfx(lin) ============================================================================== * Two Stage Least Squares (2SLS) ============================================================================== y1 = y2 + x1 + x2 ------------------------------------------------------------------------------ Ridge k Value = 0.04629 | Generalized Ridge Regression ------------------------------------------------------------------------------ Sample Size = 17 Wald Test = 76.3982 | P-Value > Chi2(3) = 0.0000 F-Test = 25.4661 | P-Value > F(3 , 13) = 0.0000 (Buse 1973) R2 = 0.8526 | Raw Moments R2 = 0.9952 (Buse 1973) R2 Adj = 0.8186 | Raw Moments R2 Adj = 0.9941 Root MSE (Sigma) = 10.4595 | Log Likelihood Function = -61.7495 ------------------------------------------------------------------------------ - R2h= 0.8528 R2h Adj= 0.8188 F-Test = 25.10 P-Value > F(3 , 13) 0.0000 - R2v= 0.8339 R2v Adj= 0.7956 F-Test = 21.76 P-Value > F(3 , 13) 0.0000 ------------------------------------------------------------------------------ y1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- y2 | .2967317 .1638088 1.81 0.093 -.0571557 .6506192 x1 | .1904857 .494348 0.39 0.706 -.8774883 1.25846 x2 | -.9198076 .2468019 -3.73 0.003 -1.452991 -.3866245 _cons | 137.0235 55.16998 2.48 0.027 17.83605 256.211 ------------------------------------------------------------------------------ * Y = LHS Dependent Variable: 1 = y1 * Yi = RHS Endogenous Variables: 1 = y2 * Xi = RHS Included Exogenous Vars: 2 = x1 x2 * Xj = RHS Excluded Exogenous Vars: 2 = x3 x4 * Z = Overall Instrumental Vars: 4 = x1 x2 x3 x4 ============================================================================== * 2SLS-IV Model Selection Diagnostic Criteria ============================================================================== - Log Likelihood Function LLF = -61.7495 --------------------------------------------------------------------------- - Akaike Information Criterion (1974) AIC = 133.9348 - Akaike Information Criterion (1973) Log AIC = 4.8974 --------------------------------------------------------------------------- - Schwarz Criterion (1978) SC = 162.9435 - Schwarz Criterion (1978) Log SC = 5.0934 --------------------------------------------------------------------------- - Amemiya Prediction Criterion (1969) FPE = 135.1436 - Hannan-Quinn Criterion (1979) HQ = 136.5705 - Rice Criterion (1984) Rice = 158.0251 - Shibata Criterion (1981) Shibata = 123.0299 - Craven-Wahba Generalized Cross Validation (1979) GCV = 143.0641 ------------------------------------------------------------------------------ * Marginal Effect - Elasticity: Linear * +---------------------------------------------------------------------------+ | Variable | Marginal_Effect(B) | Elasticity(Es) | Mean | |------------+--------------------+--------------------+--------------------| | y2 | 0.2967 | 0.3351 | 146.8118 | | x1 | 0.1905 | 0.1509 | 102.9824 | | x2 | -0.9198 | -0.5399 | 76.3118 | +---------------------------------------------------------------------------+ Mean of Dependent Variable = 130.0118 {marker 11}{bf:{err:{dlgtab:Authors}}} - {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:{col 27}{browse "http://emadstat.110mb.com/stata.htm"}} {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"}} - {hi:Sahra Khaleel A. Mickaiel} {hi:Professor (PhD Economics)} {hi:Cairo University - Faculty of Agriculture - Department of Economics - Egypt} {hi:Email: {browse "mailto:sahra_atta@hotmail.com":sahra_atta@hotmail.com}} {hi:WebPage:{col 27}{browse "http://sahraecon.110mb.com/stata.htm"}} {hi:WebPage at IDEAS:{col 27}{browse "http://ideas.repec.org/f/pmi520.html"}} {hi:WebPage at EconPapers:{col 27}{browse "http://econpapers.repec.org/RAS/pmi520.htm"}} {bf:{err:{dlgtab:RIDGE2SLS Citation}}} {p 1}{cmd:Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2013)}{p_end} {p 1 10 1}{cmd:RIDGE2SLS: "Two-Stage Least Squares (2SLS): Ridge & Weighted Regression"}{p_end} {title:Online Help:} {bf:{err:* Econometric Regression Models:}} {bf:{err:* (1) (OLS) * Ordinary Least Squares Regression Models:}} {helpb olsreg}{col 12}OLS Econometric Ridge & Weighted Regression Models: Stata Module Toolkit {helpb ridgereg}{col 12}OLS Ridge Regression Models {helpb gmmreg}{col 12}OLS Generalized Method of Moments (GMM): Ridge & Weighted Regression {helpb chowreg}{col 12}OLS Structural Change Regressions and Chow Test --------------------------------------------------------------------------- {bf:{err:* (2) (2SLS-IV) * Two-Stage Least Squares & Instrumental Variables Regression Models:}} {helpb reg2}{col 12}2SLS-IV Econometric Ridge & Weighted Regression Models: Stata Module Toolkit {helpb gmmreg2}{col 12}2SLS-IV Generalized Method of Moments (GMM): Ridge & Weighted Regression {helpb limlreg2}{col 12}Limited-Information Maximum Likelihood (LIML) IV Regression {helpb meloreg2}{col 12}Minimum Expected Loss (MELO) IV Regression {helpb ridgereg2}{col 12}Ridge 2SLS-LIML-GMM-MELO-Fuller-kClass IV Regression {helpb ridge2sls}{col 12}Two-Stage Least Squares Ridge Regression {helpb ridgegmm}{col 12}Generalized Method of Moments (GMM) IV Ridge Regression {helpb ridgeliml}{col 12}Limited-Information Maximum Likelihood (LIML) IV Ridge Regression {helpb ridgemelo}{col 12}Minimum Expected Loss (MELO) IV Ridge Regression --------------------------------------------------------------------------- {bf:{err:* (3) * Panel Data Regression Models:}} {helpb regxt}{col 12}Panel Data Econometric Ridge & Weighted Regression Models: Stata Module Toolkit {helpb xtregdhp}{col 12}Han-Philips (2010) Linear Dynamic Panel Data Regression {helpb xtregam}{col 12}Amemiya Random-Effects Panel Data: Ridge & Weighted Regression {helpb xtregbem}{col 12}Between-Effects Panel Data: Ridge & Weighted Regression {helpb xtregbn}{col 12}Balestra-Nerlove Random-Effects Panel Data: Ridge & Weighted Regression {helpb xtregfem}{col 12}Fixed-Effects Panel Data: Ridge & Weighted Regression {helpb xtregmle}{col 12}Trevor Breusch MLE Random-Effects Panel Data: Ridge & Weighted Regression {helpb xtregrem}{col 12}Fuller-Battese GLS Random-Effects Panel Data: Ridge & Weighted Regression {helpb xtregsam}{col 12}Swamy-Arora Random-Effects Panel Data: Ridge & Weighted Regression {helpb xtregwem}{col 12}Within-Effects Panel Data: Ridge & Weighted Regression {helpb xtregwhm}{col 12}Wallace-Hussain Random-Effects Panel Data: Ridge & Weighted Regression {helpb xtreghet}{col 12}MLE Random-Effects Multiplicative Heteroscedasticity Panel Data Regression --------------------------------------------------------------------------- {bf:{err:* (4) (MLE) * Maximum Likelihood Estimation Regression Models:}} {helpb mlereg}{col 12}MLE Econometric Regression Models: Stata Module Toolkit {helpb mleregn}{col 12}MLE Normal Regression {helpb mleregln}{col 12}MLE Log Normal Regression {helpb mlereghn}{col 12}MLE Half Normal Regression {helpb mlerege}{col 12}MLE Exponential Regression {helpb mleregle}{col 12}MLE Log Exponential Regression {helpb mleregg}{col 12}MLE Gamma Regression {helpb mlereglg}{col 12}MLE Log Gamma Regression {helpb mlereggg}{col 12}MLE Generalized Gamma Regression {helpb mlereglgg}{col 12}MLE Log Generalized Gamma Regression {helpb mleregb}{col 12}MLE Beta Regression {helpb mleregev}{col 12}MLE Extreme Value Regression {helpb mleregw}{col 12}MLE Weibull Regression {helpb mlereglw}{col 12}MLE Log Weibull Regression {helpb mleregilg}{col 12}MLE Inverse Log Gauss Regression --------------------------------------------------------------------------- {bf:{err:* (5) * Autocorrelation Regression Models:}} {helpb autoreg}{col 12}Autoregressive Least Squares Regression Models: Stata Module Toolkit {helpb alsmle}{col 12}Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation Regression {helpb automle}{col 12}Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation Regression {helpb autopagan}{col 12}Pagan AR(p) Conditional Autoregressive Least Squares Regression {helpb autoyw}{col 12}Yule-Walker AR(p) Unconditional Autoregressive Least Squares Regression {helpb autopw}{col 12}Prais-Winsten AR(p) Autoregressive Least Squares Regression {helpb autoco}{col 12}Cochrane-Orcutt AR(p) Autoregressive Least Squares Regression {helpb autofair}{col 12}Fair AR(1) Autoregressive Least Squares Regression --------------------------------------------------------------------------- {bf:{err:* (6) * Heteroscedasticity Regression Models:}} {helpb hetdep}{col 12}MLE Dependent Variable Heteroscedasticity {helpb hetmult}{col 12}MLE Multiplicative Heteroscedasticity Regression {helpb hetstd}{col 12}MLE Standard Deviation Heteroscedasticity Regression {helpb hetvar}{col 12}MLE Variance Deviation Heteroscedasticity Regression {helpb glsreg}{col 12}Generalized Least Squares Regression --------------------------------------------------------------------------- {bf:{err:* (7) * Non Normality Regression Models:}} {helpb robgme}{col 12}MLE Robust Generalized Multivariate Error t Distribution {helpb bcchreg}{col 12}Classical Box-Cox Multiplicative Heteroscedasticity Regression {helpb bccreg}{col 12}Classical Box-Cox Regression {helpb bcereg}{col 12}Extended Box-Cox Regression --------------------------------------------------------------------------- {bf:{err:* (8) (NLS) * Nonlinear Least Squares Regression Regression Models:}} {helpb autonls}{col 12}Non Linear Autoregressive Least Squares Regression {helpb qregnls}{col 12}Non Linear Quantile Regression --------------------------------------------------------------------------- {bf:{err:* (9) * Logit Regression Models:}} {helpb logithetm}{col 12}Logit Multiplicative Heteroscedasticity Regression {helpb mnlogit}{col 12}Multinomial Logit Regression --------------------------------------------------------------------------- {bf:{err:* (10) * Probit Regression Models:}} {helpb probithetm}{col 12}Probit Multiplicative Heteroscedasticity Regression {helpb mnprobit}{col 12}Multinomial Probit Regression --------------------------------------------------------------------------- {bf:{err:* (11) * Tobit Regression Models:}} {helpb tobithetm}{col 12}Tobit Multiplicative Heteroscedasticity Regression --------------------------------------------------------------------------- {bf:{err:* Multicollinearity Tests:}} {helpb lmcol}{col 12}OLS Multicollinearity Diagnostic Tests {helpb fgtest}{col 12}Farrar-Glauber Multicollinearity Chi2, F, t Tests {helpb theilr2}{col 12}Theil R2 Multicollinearity Effect --------------------------------------------------------------------------- {psee} {p_end}