```-------------------------------------------------------------------------------
help: ridgereg                                                   dialog: ridger
> eg
-------------------------------------------------------------------------------

+-------+
----+ Title +------------------------------------------------------------

ridgereg: OLS-Ridge Regression Models and Diagnostic Tests

+-------------------+
----+ Table of Contents +------------------------------------------------

Syntax
Description
Ridge Model Options
Weight Options
Weighted Variable Type Options
Options
Model Selection Diagnostic Criteria
Multicollinearity Diagnostic Tests
Saved Results
References

*** Examples

Author

+--------+
----+ Syntax +-----------------------------------------------------------

ridgereg depvar indepvars [if] [in] , model(orr|grr1|grr2|grr3)

[ weights(yh|yh2|abse|e2|le2|x|xi|x2|xi2) wvar(varname)

kr(#) lmcol diag dn tolog mfx(lin, log) noconstant

predict(new_var) resid(new_var) coll level(#) ]

+-------------+
----+ Description +------------------------------------------------------

ridgereg estimates (OLS-Ridge Regression models, and computes many tests,
i.e., Mmulticollinearity Tests, and Model Selection Diagnostic Criteria,
and Marginal Effects and Elasticities.

R2, R2 Adjusted, and F-Test, are obtained from 4 ways:

1- (Buse 1973) R2.
2- Raw Moments R2.
3- squared correlation between predicted (Yh) and observed dependent
variable (Y).
4- Ratio of variance between predicted (Yh) and observed dependent
variable (Y).

- Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1).
- F-Test=R2/(1-R2)*(N-K-1)/(K).

+---------------------+
----+ Ridge Model Options +----------------------------------------------

kr(#) Ridge k value, must be in the range (0 < k < 1).

IF kr(0) in ridge(orr, grr1, grr2, grr3), the model will be an OLS
regression.

model(orr) : Ordinary Ridge Regression    [Judge,et al(1988,p.878) eq.21.4.2]
> .
model(grr1): Generalized Ridge Regression [Judge,et al(1988,p.881) eq.21.4.12
> ].
model(grr2): Iterative Generalized Ridge  [Judge,et al(1988,p.881) eq.21.4.12
> ].
model(grr3): Adaptive Generalized Ridge   [Strawderman(1978)].

ridgereg estimates Ordinary Ridge regression as a multicollinearity
remediation method.
General form of Ridge Coefficients and Covariance Matrix are:

Br = inv[X'X + kI] X'Y

Cov=Sig^2 * inv[X'X + kI] (X'X) inv[X'X + kI]

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

+----------------+
----+ Weight Options +---------------------------------------------------

wvar(varname)     Weighted Variable Name

+--------------------------------+
----+ Weighted Variable Type Options +-----------------------------------

weights Options   Description

weights(yh)       Yh - Predicted Value
weights(yh2)      Yh^2 - Predicted Value Squared
weights(abse)     abs(E) - Absolute Value of Residual
weights(e2)       E^2 - Residual Squared
weights(le2)      log(E^2) - Log Residual Squared
weights(x)        (x) Variable
weights(xi)       (1/x) Inverse Variable
weights(x2)       (x^2) Squared Variable
weights(xi2)      (1/x^2) Inverse Squared Variable

+---------+
----+ Options +----------------------------------------------------------

dn               Use (N) divisor instead of (N-K) for Degrees of Freedom (DF)

noconstant       Exclude Constant Term from Equation

predict(new_var)}Predicted values variable

resid(new_var)}Residuals values variable

mfx(lin, log)    functional form: Linear model (lin), or Log-Log model (log),
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).
- mfx(log) and tolog options must be combined, to transform variables to l
> og form.

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

coll             keep collinear variables; default is removing collinear vari
> ables.

+-------------------------------------+
----+ Model Selection Diagnostic Criteria +------------------------------

diag                          Model Selection Diagnostic Criteria

- 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

+------------------------------------+
----+ Multicollinearity Diagnostic Tests +-------------------------------

lmcol                         Multicollinearity Diagnostic Tests
* Correlation Matrix
* Multicollinearity Diagnostic Criteria
* Farrar-Glauber Multicollinearity Tests
Ho: No Multicollinearity - Ha: Multicollinearity
* (1) Farrar-Glauber Multicollinearity Chi2-Test
* (2) Farrar-Glauber Multicollinearity F-Test
* (3) Farrar-Glauber Multicollinearity t-Test
* Multicollinearity Ranges
* Determinant of |X'X|
* Theil R2 Multicollinearity Effect:
- Gleason-Staelin Q0
- Heo Range  Q1

- Multicollinearity Detection:
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.

2. High simple correlation coefficients are sufficient but not necessary
for multicollinearity.

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.

- Multicollinearity Remediation:
1. Use prior information or restrictions on the coefficients. One clever
way to do this was developed by Theil and Goldberger. See tgmixed, and
Theil(1971, pp 347-352).

2. Use additional data sources. This does not mean more of the same. It
means pooling cross section and time series.

3. Transform the data. For example, inversion or differencing.

4. Use a principal components estimator. This involves using a weighted
average of the regressors, rather than all of the regressors.

5. Another alternative regression technique is ridge regression. This
involves putting extra weight on the main diagonal of X'X.

6. Dropping troublesome RHS variables. This begs the question of
specification error.

+---------------+
----+ Saved Results +----------------------------------------------------

ridgereg saves the following in e():

*** Model Selection Diagnostic Criteria:
e(N)            number of observations
e(r2bu)         R-squared (Buse 1973)
e(r2bu_a)       R-squared Adj (Buse 1973)
e(r2raw)        Raw Moments R2
e(r2raw_a)      Raw Moments R2 Adj
e(f)            F-test
e(fp)           F-test P-Value
e(wald)         Wald-test
e(waldp)        Wald-test P-Value
e(r2h)          R2 Between Predicted (Yh) and Observed DepVar (Y)
e(r2h_a)        Adjusted r2h
e(fh)           F-test due to r2h
e(fhp)          F-test due to r2h P-Value

e(llf)          Log Likelihood Function                   LLF
e(aic)          Akaike Information Criterion              (1974) AIC
e(laic)         Akaike Information Criterion              (1973) Log AIC
e(sc)           Schwarz Criterion                         (1978) SC
e(lsc)          Schwarz Criterion                         (1978) Log SC
e(fpe)          Amemiya Prediction Criterion              (1969) FPE
e(hq)           Hannan-Quinn Criterion                    (1979) HQ
e(rice)         Rice Criterion                            (1984) Rice
e(shibata)      Shibata Criterion                         (1981) Shibata
e(gcv)          Craven-Wahba Generalized Cross Validation (1979) GCV

Matrixes
e(b)            coefficient vector
e(V)            variance-covariance matrix of the estimators
e(mfxlin)       Marginal Effect and Elasticity in Lin Form
e(mfxlog)       Marginal Effect and Elasticity in Log Form

+------------+
----+ References +-------------------------------------------------------

D. Belsley (1991) "Conditioning Diagnostics, Collinearity and Weak Data
in Regression", John Wiley & Sons, Inc., New York, USA.

D. Belsley, E. Kuh, and R. Welsch (1980) "Regression Diagnostics:
Identifying Influential Data and Sources of Collinearity", John Wiley
& Sons, Inc., New York, USA.

Damodar Gujarati (1995) "Basic Econometrics" 3rd Edition, McGraw Hill,
New York, USA.

Evagelia, Mitsaki (2011) "Ridge Regression Analysis of Collinear Data",
http://www.stat-athens.aueb.gr/~jpan/diatrives/Mitsaki/chapter2.pdf

Farrar, D. and Glauber, R. (1976) "Multicollinearity in Regression
Analysis: the Problem Revisited", Review of Economics and Statistics,
49; 92-107.

Greene, William (1993) "Econometric Analysis", 2nd ed., Macmillan
Publishing Company Inc., New York, USA; 616-618.

Greene, William (2007) "Econometric Analysis", 6th ed., Upper Saddle
River, NJ: Prentice-Hall; 387-388.

Hoerl A. E. (1962) "Application of Ridge Analysis to Regression
Problems", Chemical Engineering Progress, 58; 54-59.

Hoerl, A. E. and R. W. Kennard (1970a) "Ridge Regression: Biased
Estimation for Non-Orthogonal Problems", Technometrics, 12; 55-67.

Hoerl, A. E. and R. W. Kennard (1970b) "Ridge Regression: Applications to
Non-Orthogonal Problems", Technometrics, 12; 69-82.

Hoerl, A. E. ,R. W. Kennard, & K. Baldwin (1975) "Ridge Regression: Some
Simulations", Communications in Statistics, A, 4; 105-123.

Hoerl, A. E. and R. W. Kennard (1976) "Ridge Regression: Iterative
Estimation of the Biasing Parameter", Communications in Statistics,
A, 5; 77-88.

Marquardt D.W. (1970) "Generalized Inverses, Ridge Regression, Biased
Linear Estimation, and Nonlinear Estimation", Technometrics, 12;
591-612.

Marquardt D.W. & R. Snee (1975) "Ridge Regression in Practice", The
American Statistician, 29; 3-19.

Pidot, George (1969) "A Principal Components Analysis of the Determinants
of Local Government Fiscal Patterns", Review of Economics and
Statistics, Vol. 51; 176-188.

Rencher, Alvin C. (1998) "Multivariate Statistical Inference and
Applications", John Wiley & Sons, Inc., New York, USA; 21-22.

Strawderman, W. E. (1978) "Minimax Adaptive Generalized Ridge Regression
Estimators", Journal American Statistical Association, 73; 623-627.

Theil, Henri (1971) "Principles of Econometrics", John Wiley & Sons,
Inc., New York, USA.

+----------+
----+ Examples +---------------------------------------------------------

(1) Example of Ridge regression models,
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.

clear all

sysuse ridgereg1.dta, clear

ridgereg y x1 x2 x3 , model(orr) kr(0.5) mfx(lin) lmcol diag

ridgereg y x1 x2 x3 , model(orr) kr(0.5) mfx(lin) weights(x) wvar(x1)

ridgereg y x1 x2 x3 , model(grr1) mfx(lin)

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

ridgereg y x1 x2 x3 , model(grr3) mfx(lin)

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

clear all

sysuse ridgereg2.dta, clear

ridgereg y x1 x2 x3 x4 x5 , model(orr) lmcol

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

clear all

sysuse ridgereg3.dta, clear

ridgereg y x1 x2 x3 x4 x5 x6 , model(orr) lmcol
-------------------------------------------------------------------------------

. clear all
. sysuse ridgereg1.dta , clear
. ridgereg y x1 x2 x3 , model(orr) kr(0) diag lmcol mfx(lin)

==============================================================================
* (OLS) Ridge Regression - Ordinary Ridge Regression
==============================================================================
y = x1 + x2 + x3
------------------------------------------------------------------------------
Ridge k Value     =   0.00000     |   Ordinary Ridge Regression
------------------------------------------------------------------------------
Sample Size       =          20
Wald Test         =    322.1130   |   P-Value > Chi2(3)       =      0.0000
F-Test            =    107.3710   |   P-Value > F(3 , 16)     =      0.0000
(Buse 1973) R2     =      0.9527   |   Raw Moments R2          =      0.9971
(Buse 1973) R2 Adj =      0.9438   |   Raw Moments R2 Adj      =      0.9965
Root MSE (Sigma)  =      4.5272   |   Log Likelihood Function =    -56.3495
------------------------------------------------------------------------------
- R2h= 0.9527   R2h Adj= 0.9438  F-Test =  107.37 P-Value > F(3 , 16)  0.0000
- R2v= 0.9527   R2v Adj= 0.9438  F-Test =  107.37 P-Value > F(3 , 16)  0.0000
------------------------------------------------------------------------------
y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 |   1.058783    .173579     6.10   0.000     .6908121    1.426754
x2 |   .4522435   .6557569     0.69   0.500    -.9378991    1.842386
x3 |   .1211505   1.087042     0.11   0.913    -2.183275    2.425576
_cons |   8.132845   8.921103     0.91   0.375    -10.77905    27.04474
------------------------------------------------------------------------------

==============================================================================
* OLS Model Selection Diagnostic Criteria - Model= (orr)
==============================================================================
- Log Likelihood Function       LLF             =    -56.3495
- Akaike Final Prediction Error AIC             =     22.1330
- Schwarz Criterion             SC              =     25.6984
- Akaike Information Criterion  ln AIC          =      3.0971
- Schwarz Criterion             ln SC           =      3.2464
- Amemiya Prediction Criterion  FPE             =     23.5700
- Hannan-Quinn Criterion        HQ              =     22.7878
- Rice Criterion                Rice            =     23.4236
- Shibata Criterion             Shibata         =     21.3155
- Craven-Wahba Generalized Cross Validation GCV =     22.6941
------------------------------------------------------------------------------

==============================================================================
*** Multicollinearity Diagnostic Tests - Model= (orr)
==============================================================================

* Correlation Matrix
(obs=20)

|       x1       x2       x3
-------------+---------------------------
x1 |   1.0000
x2 |   0.7185   1.0000
x3 |   0.9152   0.6306   1.0000

* Multicollinearity Diagnostic Criteria
+------------------------------------------------------------------------------
> -+
|   Var |  Eigenval |  C_Number |   C_Index |       VIF |     1/VIF |   R2_xi,X
>  |
|-------+-----------+-----------+-----------+-----------+-----------+----------
> -|
|    x1 |    2.5160 |    1.0000 |    1.0000 |    7.7349 |    0.1293 |    0.8707
>  |
|    x2 |    0.4081 |    6.1651 |    2.4830 |    2.0862 |    0.4793 |    0.5207
>  |
|    x3 |    0.0758 |   33.1767 |    5.7599 |    6.2127 |    0.1610 |    0.8390
>  |
+------------------------------------------------------------------------------
> -+

* Farrar-Glauber Multicollinearity Tests
Ho: No Multicollinearity - Ha: Multicollinearity
--------------------------------------------------

* (1) Farrar-Glauber Multicollinearity Chi2-Test:
Chi2 Test =   43.8210    P-Value > Chi2(3) 0.0000

* (2) Farrar-Glauber Multicollinearity F-Test:
+--------------------------------------------------------+
|   Variable |   F_Test |      DF1 |      DF2 |  P_Value |
|------------+----------+----------+----------+----------|
|         x1 |   57.246 |   17.000 |    3.000 |    0.003 |
|         x2 |    9.233 |   17.000 |    3.000 |    0.046 |
|         x3 |   44.308 |   17.000 |    3.000 |    0.005 |
+--------------------------------------------------------+

* (3) Farrar-Glauber Multicollinearity t-Test:
+-------------------------------------+
| Variable |     x1 |     x2 |     x3 |
|----------+--------+--------+--------|
|       x1 |      . |        |        |
|       x2 |  4.259 |      . |        |
|       x3 |  9.362 |  3.350 |      . |
+-------------------------------------+

* |X'X| Determinant:
|X'X| = 0 Multicollinearity - |X'X| = 1 No Multicollinearity
|X'X| Determinant:       (0 < 0.0779 < 1)
---------------------------------------------------------------

* Theil R2 Multicollinearity Effect:
R2 = 0 No Multicollinearity - R2 = 1 Multicollinearity
- Theil R2:           (0 < 0.8412 < 1)
---------------------------------------------------------------

* Multicollinearity Range:
Q = 0 No Multicollinearity - Q = 1 Multicollinearity
- Gleason-Staelin Q0: (0 < 0.7641 < 1)
1- Heo Range Q1:       (0 < 0.8581 < 1)
2- Heo Range Q2:       (0 < 0.8129 < 1)
3- Heo Range Q3:       (0 < 0.7209 < 1)
4- Heo Range Q4:       (0 < 0.7681 < 1)
5- Heo Range Q5:       (0 < 0.8798 < 1)
6- Heo Range Q6:       (0 < 0.7435 < 1)
------------------------------------------------------------------------------

* Marginal Effect - Elasticity (Model= orr): Linear *

+---------------------------------------------------------------------------+
|   Variable | Marginal_Effect(B) |     Elasticity(Es) |               Mean |
|------------+--------------------+--------------------+--------------------|
|         x1 |             1.0588 |             0.7683 |            52.5840 |
|         x2 |             0.4522 |             0.1106 |            17.7245 |
|         x3 |             0.1212 |             0.0088 |             5.2935 |
+---------------------------------------------------------------------------+
Mean of Dependent Variable =     72.4650

+--------+
----+ Author +-----------------------------------------------------------

Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Eg
> ypt
Email: emadstat@hotmail.com
WebPage:                http://emadstat.110mb.com/stata.htm
WebPage at IDEAS:       http://ideas.repec.org/f/psh494.html
WebPage at EconPapers:  http://econpapers.repec.org/RAS/psh494.htm

+-------------------+
----+ RIDGEREG Citation +------------------------------------------------

Shehata, Emad Abd Elmessih (2012)
RIDGEREG: "OLS-Ridge Regression Models and Diagnostic Tests"

http://ideas.repec.org/c/boc/bocode/s457347.html

http://econpapers.repec.org/software/bocbocode/s457347.htm

Online Help:

* Econometric Regression Models:

* (1) (OLS) * Ordinary Least Squares Regression Models:
olsreg     OLS Econometric Ridge & Weighted Regression Models: Stata Module Too
> lkit
ridgereg   OLS Ridge Regression Models
gmmreg     OLS Generalized Method of Moments (GMM): Ridge & Weighted Regression
chowreg    OLS Structural Change Regressions and Chow Test
---------------------------------------------------------------------------
* (2) (2SLS-IV) * Two-Stage Least Squares & Instrumental Variables Regression M
> odels:
reg2       2SLS-IV Econometric Ridge & Weighted Regression Models: Stata Module
>  Toolkit
gmmreg2    2SLS-IV Generalized Method of Moments (GMM): Ridge & Weighted Regres
> sion
limlreg2   Limited-Information Maximum Likelihood (LIML) IV Regression
meloreg2   Minimum Expected Loss (MELO) IV Regression
ridgereg2  Ridge 2SLS-LIML-GMM-MELO-Fuller-kClass IV Regression
ridge2sls  Two-Stage Least Squares Ridge Regression
ridgegmm   Generalized Method of Moments (GMM) IV Ridge Regression
ridgeliml  Limited-Information Maximum Likelihood (LIML) IV Ridge Regression
ridgemelo  Minimum Expected Loss (MELO) IV Ridge Regression
---------------------------------------------------------------------------
* (3) * Panel Data Regression Models:
regxt      Panel Data Econometric Ridge & Weighted Regression Models: Stata Mod
> ule Toolkit
xtregdhp   Han-Philips (2010) Linear Dynamic Panel Data Regression
xtregam    Amemiya Random-Effects Panel Data: Ridge & Weighted Regression
xtregbem   Between-Effects Panel Data: Ridge & Weighted Regression
xtregbn    Balestra-Nerlove Random-Effects Panel Data: Ridge & Weighted Regress
> ion
xtregfem   Fixed-Effects Panel Data: Ridge & Weighted Regression
xtregmle   Trevor Breusch MLE Random-Effects Panel Data: Ridge & Weighted Regre
> ssion
xtregrem   Fuller-Battese GLS Random-Effects Panel Data: Ridge & Weighted Regre
> ssion
xtregsam   Swamy-Arora Random-Effects Panel Data: Ridge & Weighted Regression
xtregwem   Within-Effects Panel Data: Ridge & Weighted Regression
xtregwhm   Wallace-Hussain Random-Effects Panel Data: Ridge & Weighted Regressi
> on
xtreghet   MLE Random-Effects Multiplicative Heteroscedasticity Panel Data Regr
> ession
---------------------------------------------------------------------------
* (4) (MLE) * Maximum Likelihood Estimation Regression Models:
mlereg     MLE Econometric Regression Models: Stata Module Toolkit
mleregn    MLE Normal Regression
mleregln   MLE Log Normal Regression
mlereghn   MLE Half Normal Regression
mlerege    MLE Exponential Regression
mleregle   MLE Log Exponential Regression
mleregg    MLE Gamma Regression
mlereglg   MLE Log Gamma Regression
mlereggg   MLE Generalized Gamma Regression
mlereglgg  MLE Log Generalized Gamma Regression
mleregb    MLE Beta Regression
mleregev   MLE Extreme Value Regression
mleregw    MLE Weibull Regression
mlereglw   MLE Log Weibull Regression
mleregilg  MLE Inverse Log Gauss Regression
---------------------------------------------------------------------------
* (5) * Autocorrelation Regression Models:
autoreg    Autoregressive Least Squares Regression Models: Stata Module Toolkit
alsmle     Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation R
> egression
automle    Beach-Mackinnon AR(1) Autoregressive Maximum Likelihood Estimation R
> egression
autopagan  Pagan AR(p) Conditional Autoregressive Least Squares Regression
autoyw     Yule-Walker AR(p) Unconditional Autoregressive Least Squares Regress
> ion
autopw     Prais-Winsten AR(p) Autoregressive Least Squares Regression
autoco     Cochrane-Orcutt AR(p) Autoregressive Least Squares Regression
autofair   Fair AR(1) Autoregressive Least Squares Regression
---------------------------------------------------------------------------
* (6) * Heteroscedasticity Regression Models:
hetdep     MLE Dependent Variable Heteroscedasticity
hetmult    MLE Multiplicative Heteroscedasticity Regression
hetstd     MLE Standard Deviation Heteroscedasticity Regression
hetvar     MLE Variance Deviation Heteroscedasticity Regression
glsreg     Generalized Least Squares Regression
---------------------------------------------------------------------------
* (7) * Non Normality Regression Models:
robgme     MLE Robust Generalized Multivariate Error t Distribution
bcchreg    Classical Box-Cox Multiplicative Heteroscedasticity Regression
bccreg     Classical Box-Cox Regression
bcereg     Extended Box-Cox Regression
---------------------------------------------------------------------------
* (8) (NLS) * Nonlinear Least Squares Regression Regression Models:
autonls    Non Linear Autoregressive Least Squares Regression
qregnls    Non Linear Quantile Regression
---------------------------------------------------------------------------
* (9) * Logit Regression Models:
logithetm  Logit Multiplicative Heteroscedasticity Regression
mnlogit    Multinomial Logit Regression
---------------------------------------------------------------------------
* (10) * Probit Regression Models:
probithetm Probit Multiplicative Heteroscedasticity Regression
mnprobit   Multinomial Probit Regression
---------------------------------------------------------------------------
* (11) * Tobit Regression Models:
tobithetm  Tobit Multiplicative Heteroscedasticity Regression
---------------------------------------------------------------------------
* Multicollinearity Tests:
lmcol      OLS Multicollinearity Diagnostic Tests
fgtest     Farrar-Glauber Multicollinearity Chi2, F, t Tests
theilr2    Theil R2 Multicollinearity Effect
---------------------------------------------------------------------------

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