{smcl}
{hline}
{cmd:help: {helpb ridgereg}}{space 55} {cmd:dialog:} {bf:{dialog ridgereg}}
{hline}

{bf:{err:{dlgtab:Title}}}

{bf: ridgereg: OLS Ridge Regression Models"}

{marker 00}{bf:{err:{dlgtab:Table of Contents}}}
{p 4 8 2}

{p 5}{helpb ridgereg##01:Syntax}{p_end}
{p 5}{helpb ridgereg##02:Options}{p_end}
{p 5}{helpb ridgereg##03:Description}{p_end}
{p 5}{helpb ridgereg##04:Saved Results}{p_end}
{p 5}{helpb ridgereg##05:References}{p_end}

{p 1}*** {helpb ridgereg##06:Examples}{p_end}

{p 5}{helpb ridgereg##07:Author}{p_end}

{marker 01}{bf:{err:{dlgtab:Syntax}}}

{p 4 8 6}
{opt ridgereg} {depvar} {indepvars} {ifin} {weight} , {opt m:odel(orr|grr1|grr2|grr3)} {p_end} 
{p 8 8 6}
{err: [} {opt kr(numlist)} {opt mfx(lin|log)} {opt lm:cl} {opt diag} {opt dn} {opt weights(type)} {opt wvar(varname)}{p_end} 
{p 8 8 6}
{opt tolog} {opt pred:ict(new_var)} {opt res:id(new_var)} {opt tol:erance(#)} {opt iter(#)} {err:]}{p_end} 

{marker 02}{bf:{err:{dlgtab:Options}}}
{p 2 6 2}

{synoptset 6 tabbed}{...}
{synopthdr}
{synoptline}

{synopt :{opt kr(#)}}Ridge k value, must be in the range (0 < k < 1).{p_end}

{p 6 2 2}{opt model(orr, grr1, grr2, grr3)}.{p_end}

{p 6 2 2}{cmd:ridgereg} can estimate 4 types of Ridge Regressions family models.{p_end}

{p 6 8 6}{bf:model({err:{it:orr}})} : Ordinary Ridge Regression [Judge, et al(1988, p.878) eq.21.4.2].{p_end}
{p 6 8 6}{bf:model({err:{it:grr1}})}: Generalized Ridge Regression [Judge, et al(1988, p.881) eq.21.4.12].{p_end}
{p 6 8 6}{bf:model({err:{it:grr2}})}: Iterative Generalized Ridge Regression [Judge, et al(1988, p.881) eq.21.4.12].{p_end}
{p 6 8 6}{bf:model({err:{it:grr3}})}: Adaptive Generalized Ridge Regression [Strawderman(1978)].{p_end}

{p 6 6 2}{opt model(grr1, grr2, grr3)} and {bf:kr(#)} must be not combined.{p_end}

{p 6 6 2}IF {bf:kr(0)} in {opt model(orr, grr1, grr2, grr3)}, this means that a value of (kr = 0), so the model will be an OLS regression.{p_end}

{p 6 6 2}IF you dont set model, then OLS Regression will be estiamted.{p_end}

{p 6 6 2}{opt model(orr)} allows to set kr value that should be between zero and one (0 < kr < 1) to convert OLS regression to RIDGE regression, the diagonal elements of the X'X matrix are augmented by kr.{p_end}

{synoptset 16}{...}
{synopt:{bf:wvar({err:{it:varname}})}}Weighted Variable Name{p_end}

{synopt:{bf:weights({err:{it:varname}})}}Weighted Variable Type Options{p_end}

{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}

{synopt :{opt tolog} Convert dependent and independent variables to LOG Form in the memory for Log-Log regression. {opt tolog} Transforms {depvar} and {indepvars} to Log Form without lost the original data variables}{p_end}

{synopt :{opt iter(#)}}number of iterations; Default is iter(50){p_end}

{synopt :{opt tol:erance(#)}}tolerance for coefficient vector; Default is tol(0.00001){p_end}

{synopt :{bf:mfx({err:{it:lin, log}})}}type of functional form, either Linear model {cmd:(lin)}, or Log-Log model {cmd:(log)}, to compute Marginal Effects and Elasticities.{p_end}

{pmore}- In Linear Model Marginal Effects = Coefficients (Bm), and Elasticities =(Bm X/Y).

{pmore}- In Log-Log Model: Elasticities = Coefficients (Es), and Marginal Effects =(Es Y/X).

{synopt:{opt lmcl}}Multicollinearity Diagnostic Tests and Criteria{p_end}

	  * Correlation matrix
	  * (VIF):   Variance Inflation Factor
	  * (1/VIF): Tolerance
	  * Eigenvalues (computed from correlation matrix)
	  * (C_Number): Condition Number
	  * (C_Index):  Condition Index
	  * (R2_xi,X): R2-squared between each Xi and other independent variables

{synopt :{bf:Display Farrar-Glauber Multicollinearity tests:}}{p_end}
	  * Farrar-Glauber Multicollinearity Chi2-Test
	  * Farrar-Glauber Multicollinearity F-Test
	  * Farrar-Glauber Multicollinearity t-Test

{synopt :{bf:Display Multicollinearity Ranges:}}{p_end}
	  * Determinant of |X'X|

	  * Theil R2 Multicollinearity Effect [Theil(1971, p.179)], [Judge, et al(1988, p.870)]

	  * Gleason-Staelin Q0 Multicollinearity Range
	  * Heo Multicollinearity Range Q1
	  * Heo Multicollinearity Range Q2
	  * Heo Multicollinearity Range Q3
	  * Heo Multicollinearity Range Q4
	  * Heo Multicollinearity Range Q5
	  * Heo Multicollinearity Range Q6

{marker 03}{bf:{err:{dlgtab:Description}}}

{p 2 4 2}Ridge regression is considered 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 < kr < 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


{cmd:- Multicollinearity Detection:}
{p 2 4 2}1. A high F statistic or R2 leads to reject the joint hypothesis that all of the coefficients are zero, but individual t-statistics are low.{p_end} 
{p 2 4 2}2. High simple correlation coefficients are sufficient but not necessary for multicollinearity.{p_end} 
{p 2 4 2}3. One can compute condition number. That is, the ratio of largest to smallest root of the matrix x'x. This may not always be useful as the standard errors of the estimates depend on the ratios of elements of characteristic vectors to the roots.{p_end} 

{cmd:- Multicollinearity Remediation:}
{p 2 4 2}1. Use prior information or restrictions on the coefficients. One clever way to do this was developed by Theil and Goldberger. See {helpb tgmixed}, and Theil(1971, pp 347-352).{p_end} 
{p 2 4 2}2. Use additional data sources. This does not mean more of the same. It means pooling cross section and time series.{p_end} 
{p 2 4 2}3. Transform the data. For example, inversion or differencing.{p_end} 
{p 2 4 2}4. Use a principal components estimator. This involves using a weighted average of the regressors, rather than all of the regressors.{p_end} 
{p 2 4 2}5. Another alternative regression technique is ridge regression. This involves putting extra weight on the main diagonal of X'X.{p_end} 
{p 2 4 2}6. Dropping troublesome RHS variables. This begs the question of specification error.{p_end}

{marker 04}{bf:{err:{dlgtab:Saved Results}}}

{pstd}
{cmd:ridgereg} saves the following in {cmd:e()}:

{col 4}{cmd:e(N)}{col 20}Number of obs
{col 4}{cmd:e(r2c)}{col 20}R2
{col 4}{cmd:e(r2c_a)}{col 20}adj R2
{col 4}{cmd:e(r2cc)}{col 20}Corrected R2
{col 4}{cmd:e(r2cc_a)}{col 20}adj Corrected R2
{col 4}{cmd:e(r2u)}{col 20}Raw Moment R2
{col 4}{cmd:e(r2u_a)}{col 20}Adj Raw Moment R2
{col 4}{cmd:e(sig)}{col 20}Sigma (MSE)
{col 4}{cmd:e(wald)}{col 20}Wald Test
{col 4}{cmd:e(waldp)}{col 20}Wald Test P-Value
{col 4}{cmd:e(llf)}{col 20}Log Likelihood Function
{col 4}{cmd:e(aic)}{col 20}AKAIKE Final Prediction Error
{col 4}{cmd:e(sc)}{col 20}Schwartz Criterion
{col 4}{cmd:e(laic)}{col 20}Akaike Information Criterion  ln AIC
{col 4}{cmd:e(lsc)}{col 20}Schwarz Criterion Log SC
{col 4}{cmd:e(fpe)}{col 20}Amemiya Prediction Criterion
{col 4}{cmd:e(hq)}{col 20}Hannan-Quinn Criterion
{col 4}{cmd:e(rice)}{col 20}Rice Criterion
{col 4}{cmd:e(shibata)}{col 20}Shibata Criterion
{col 4}{cmd:e(gcv)}{col 20}Craven-Wahba Generalized Cross Validation-GCV
{col 4}{cmd:e(f)}{col 20}F Test
{col 4}{cmd:e(fp)}{col 20}F Test P-Value

{marker 05}{bf:{err:{dlgtab:References}}}

{p 4 8 2}D. Belsley (1991)
{cmd: "Conditioning Diagnostics, Collinearity and Weak Data in Regression",}
{it:John Wiley & Sons, Inc., New York, USA}.

{p 4 8 2}D. Belsley, E. Kuh, and R. Welsch (1980)
{cmd: "Regression Diagnostics: Identifying Influential Data and Sources of Collinearity",}
{it:John Wiley & Sons, Inc., 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}Farrar, D. and Glauber, R. (1976)
{cmd: "Multicollinearity in Regression Analysis: the Problem Revisited",}
{it:Review of Economics and Statistics, 49}; 92-107.

{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, William. 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}; 914-916.

{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}; 878-882.

{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 Anerican Statistician, 29}; 3-19.

{p 4 8 2}Pidot, George (1969)
{cmd: "A Principal Components Analysis of the Determinants of Local Government Fiscal Patterns",}
{it:Review of Economics and Statistics, Vol. 51}; 176-188.

{p 4 8 2}Rencher, Alvin C. (1998)
{cmd: "Multivariate Statistical Inference and Applications",}
{it:John Wiley & Sons, Inc., New York, USA}; 21-22.

{p 4 8 2}Strawderman, W. E. (1978)
{cmd: "Minimax Adaptive Generalized Ridge Regression Estimators",}
{it:Journal American Statistical Association, 73}; 623-627.

{p 4 8 2}Theil, Henri (1971)
{cmd: "Principles of Econometrics",}
{it:John Wiley & Sons, Inc., New York, USA}.

{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 06}{bf:{err:{dlgtab:Examples}}}

{p 2 4 2}(1) Example of Ridge regression models,{p_end}
{p 6 6 2}is decribed in: [Judge, et al(1988, p.882)], and also Theil R2 Multicollinearity Effect in: [Judge, et al(1988, p.872)], for Klein-Goldberger data.{p_end}

	{stata clear all}

	{stata sysuse ridgereg1.dta, clear}

	{stata ridgereg y x1 x2 x3 , lmcl diag}

	{stata ridgereg y x1 x2 x3 , model(orr) kr(0.5) lmcl diag}

	{stata ridgereg y x1 x2 x3 , model(grr1)}

	{stata ridgereg y x1 x2 x3 , model(grr2)}

	{stata ridgereg y x1 x2 x3 , model(grr3)}

	{stata ridgereg y x1 x2 x3 , model(grr2) mfx(lin)}

{p 2 4 4}(2) Example of Gleason-Staelin, and Heo Multicollinearity Ranges,{p_end}
{p 6 6 2}is decribed in: [Rencher(1998, pp. 20-22)].{p_end}

	{stata clear all}

	{stata sysuse ridgereg2.dta, clear}

	{stata ridgereg y x1 x2 x3 x4 x5 , lmcl}

{p 2 4 4}(3) Example of Farrar-Glauber Multicollinearity Chi2, F, t Tests{p_end}
{p 6 6 2}is decribed in:[Evagelia(2011, chap.2, p.23)].{p_end}

	{stata clear all}

	{stata sysuse ridgereg3.dta, clear}

	{stata ridgereg y x1 x2 x3 x4 x5 x6 , lmcl}

{marker 07}{bf:{err:{dlgtab:Author}}}

  {hi:Emad Abd Elmessih Shehata}
  {hi:Assistant Professor}
  {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"}}

{bf:{err:{dlgtab:ridgereg Citation}}}

{phang}Shehata, Emad Abd Elmessih (2011){p_end}
{phang}{cmd:RIDGEREG: "Stata Module to Estimate OLS Ridge Regression Models"}{p_end}

	{browse "http://ideas.repec.org/c/boc/bocode/s457347.html"}

	{browse "http://econpapers.repec.org/software/bocbocode/s457347.htm"}

{title:Also see}

{p 4 12 2}Online: {helpb ridgereg}, {helpb tgmixed}, {helpb ridge2sls}, {helpb ridgeliml}, {helpb ridgegmm}, {helpb ridgemelo}, (if installed).{p_end}

{psee}
{p_end}