Variance Covariance Matrix of Sureg in Stata

[Melody Brown]

Hi everyone,

I have a question about how to display the variance-covariance matrix for the residuals when using sureg in Stata. I know that corr option can give a correlation matrix, but what we want is a variance-covariance matrix and we wonder if anyone knows how to realize this in Stata?

Thanks a lot!

[Clyde Schechter]

If you mean the variance-covariance matrix of the estimators, you can see it with -estat vce-.

[Joseph Coveney]

how to display the variance-covariance matrix for the residuals when using sureg in Stata.

According to the help file for sureg it's among the list of objects that are ereturned: " e(Sigma) Sigma hat, covariance matrix of residuals".

It seems accurate.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ565332290

.ÿ
.ÿtempnameÿCov

.ÿmatrixÿdefineÿ`Cov'ÿ=ÿ100,ÿ-25ÿ\ÿ-25,ÿ50

.ÿ
.ÿquietlyÿdrawnormÿe1ÿe2,ÿdoubleÿcov(`Cov')ÿn(1000)

.ÿ
.ÿsuregÿ(e1ÿ)ÿ(e2ÿ)

Seeminglyÿunrelatedÿregression
------------------------------------------------------------------------------
EquationÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿÿÿParamsÿÿÿÿÿÿÿÿÿRMSEÿÿ"R-squared"ÿÿÿÿÿÿchi2ÿÿÿP>chi2
------------------------------------------------------------------------------
e1ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1,000ÿÿÿÿÿÿÿÿ1ÿÿÿÿÿ10.17879ÿÿÿÿÿÿ0.0000ÿÿÿÿÿÿÿ0.04ÿÿÿ0.8348
e2ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1,000ÿÿÿÿÿÿÿÿ1ÿÿÿÿÿ7.025012ÿÿÿÿÿÿ0.0000ÿÿÿÿÿÿÿ3.49ÿÿÿ0.0619
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
e1ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0671311ÿÿÿ.3218815ÿÿÿÿ-0.21ÿÿÿ0.835ÿÿÿÿ-.6980073ÿÿÿÿ.5637451
-------------+----------------------------------------------------------------
e2ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4147558ÿÿÿ.2221504ÿÿÿÿ-1.87ÿÿÿ0.062ÿÿÿÿ-.8501625ÿÿÿÿÿ.020651
------------------------------------------------------------------------------

.ÿmatrixÿlistÿe(Sigma)

symmetricÿe(Sigma)[2,2]
ÿÿÿÿÿÿÿÿÿÿÿÿe1ÿÿÿÿÿÿÿÿÿÿe2
e1ÿÿÿ103.60772
e2ÿÿ-26.043198ÿÿÿ49.350798

.ÿ
.ÿexit

endÿofÿdo-file


.

[Melody Brown]

According to the help file for sureg it's among the list of objects that are ereturned: " e(Sigma) Sigma hat, covariance matrix of residuals".

It seems accurate.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ565332290

.ÿ
.ÿtempnameÿCov

.ÿmatrixÿdefineÿ`Cov'ÿ=ÿ100,ÿ-25ÿ\ÿ-25,ÿ50

.ÿ
.ÿquietlyÿdrawnormÿe1ÿe2,ÿdoubleÿcov(`Cov')ÿn(1000)

.ÿ
.ÿsuregÿ(e1ÿ)ÿ(e2ÿ)

Seeminglyÿunrelatedÿregression
------------------------------------------------------------------------------
EquationÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿÿÿParamsÿÿÿÿÿÿÿÿÿRMSEÿÿ"R-squared"ÿÿÿÿÿÿchi2ÿÿÿP>chi2
------------------------------------------------------------------------------
e1ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1,000ÿÿÿÿÿÿÿÿ1ÿÿÿÿÿ10.17879ÿÿÿÿÿÿ0.0000ÿÿÿÿÿÿÿ0.04ÿÿÿ0.8348
e2ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1,000ÿÿÿÿÿÿÿÿ1ÿÿÿÿÿ7.025012ÿÿÿÿÿÿ0.0000ÿÿÿÿÿÿÿ3.49ÿÿÿ0.0619
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
e1ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0671311ÿÿÿ.3218815ÿÿÿÿ-0.21ÿÿÿ0.835ÿÿÿÿ-.6980073ÿÿÿÿ.5637451
-------------+----------------------------------------------------------------
e2ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4147558ÿÿÿ.2221504ÿÿÿÿ-1.87ÿÿÿ0.062ÿÿÿÿ-.8501625ÿÿÿÿÿ.020651
------------------------------------------------------------------------------

.ÿmatrixÿlistÿe(Sigma)

symmetricÿe(Sigma)[2,2]
ÿÿÿÿÿÿÿÿÿÿÿÿe1ÿÿÿÿÿÿÿÿÿÿe2
e1ÿÿÿ103.60772
e2ÿÿ-26.043198ÿÿÿ49.350798

.ÿ
.ÿexit

endÿofÿdo-file


.

Thanks a lot, Joseph! This is exactly what I want

[Melody Brown]

If you mean the variance-covariance matrix of the estimators, you can see it with -estat vce-.

Hi Clyde,

Thank you very much for your reply. I'll check the command

[Melody Brown]

Hi everyone,

I have a question about how to display the variance-covariance matrix for the residuals when using sureg in Stata. I know that corr option can give a correlation matrix, but what we want is a variance-covariance matrix and we wonder if anyone knows how to realize this in Stata?

Thanks a lot!

Hi Clyde and Joseph,

I have an additional question: I wonder for this e(Sigma) option can we add anything else to show the significance of the covariances between the residuals?

Please let me know if you have any thoughts on this.

Thanks

[Joseph Coveney]

for this e(Sigma) option can we add anything else to show the significance of the covariances between the residuals?

Please let me know if you have any thoughts on this.

Not that I'm aware of, but then I don't use sureg.

You can probably get at it by predicting the residuals for each equation and using something like pwcorr. It's illustrated below, along with a likelihood-ratio test of the same thing using sem to fit a covariance term for the residuals of the two equations.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿsysuseÿauto

.ÿ
.ÿsuregÿ(mpgÿc.weight)ÿ(headroomÿc.length),ÿnoheader

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
mpgÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿweightÿ|ÿÿÿ-.006009ÿÿÿ.0005108ÿÿÿ-11.76ÿÿÿ0.000ÿÿÿÿ-.0070102ÿÿÿ-.0050078
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ39.44121ÿÿÿ1.592028ÿÿÿÿ24.77ÿÿÿ0.000ÿÿÿÿÿ36.32089ÿÿÿÿ42.56153
-------------+----------------------------------------------------------------
headroomÿÿÿÿÿ|
ÿÿÿÿÿÿlengthÿ|ÿÿÿ.0195919ÿÿÿ.0037825ÿÿÿÿÿ5.18ÿÿÿ0.000ÿÿÿÿÿ.0121783ÿÿÿÿ.0270055
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6887166ÿÿÿ.7157624ÿÿÿÿ-0.96ÿÿÿ0.336ÿÿÿÿ-2.091585ÿÿÿÿ.7141519
------------------------------------------------------------------------------

.ÿ
.ÿ//ÿOneÿmethod,ÿquickÿandÿdirty,ÿperhaps
.ÿpredictÿdoubleÿe_mpg,ÿresidualsÿeq(#1)

.ÿpredictÿdoubleÿe_hea,ÿresidualsÿeq(#2)

.ÿpwcorrÿe_*,ÿsig

ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿe_mpgÿÿÿÿe_hea
-------------+------------------
ÿÿÿÿÿÿÿe_mpgÿ|ÿÿÿ1.0000ÿ
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿe_heaÿ|ÿÿ-0.0138ÿÿÿ1.0000ÿ
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿ0.9071
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|

.ÿ
.ÿ//ÿAlternative,ÿmaybeÿmoreÿprincipled
.ÿsemÿ(e_mpgÿ)ÿ(e_heaÿ),ÿ///
>ÿÿÿÿÿÿÿÿÿnocnsreportÿnodescribeÿnofootnoteÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ74
Estimationÿmethod:ÿml

Logÿlikelihoodÿ=ÿ-276.03339

---------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
----------------+----------------------------------------------------------------
ÿÿÿÿÿmean(e_mpg)|ÿÿÿ5.72e-14ÿÿÿ.3943236ÿÿÿÿÿ0.00ÿÿÿ1.000ÿÿÿÿÿÿ-.77286ÿÿÿÿÿÿ.77286
ÿÿÿÿÿmean(e_hea)|ÿÿ-2.80e-14ÿÿÿ.0836526ÿÿÿÿ-0.00ÿÿÿ1.000ÿÿÿÿ-.1639561ÿÿÿÿ.1639561
----------------+----------------------------------------------------------------
ÿÿÿÿÿÿvar(e_mpg)|ÿÿÿ11.50634ÿÿÿ1.891631ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ8.336823ÿÿÿÿ15.88086
ÿÿÿÿÿÿvar(e_hea)|ÿÿÿ.5178342ÿÿÿ.0851314ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3751924ÿÿÿÿÿ.714706
----------------+----------------------------------------------------------------
cov(e_mpg,e_hea)|ÿÿ-.0336703ÿÿÿÿ.283785ÿÿÿÿ-0.12ÿÿÿ0.906ÿÿÿÿ-.5898787ÿÿÿÿ.5225381
---------------------------------------------------------------------------------

.ÿestimatesÿstoreÿCovariance

.ÿ
.ÿquietlyÿsemÿ(e_mpgÿ)ÿ(e_heaÿ),ÿcovariance(e_mpg*e_hea@0)ÿ

.ÿlrtestÿCovariance

Likelihood-ratioÿtest
Assumption:ÿ.ÿnestedÿwithinÿCovariance

ÿLRÿchi2(1)ÿ=ÿÿÿ0.01
Probÿ>ÿchi2ÿ=ÿ0.9055

.ÿ
.ÿexit

endÿofÿdo-file


.

If you're that interested in some kind of null hypothesis significance test that the covariance of the residuals is exactly zero, then maybe fit a model using sem or gsem from the beginning.

[Melody Brown]

Not that I'm aware of, but then I don't use sureg.

You can probably get at it by predicting the residuals for each equation and using something like pwcorr. It's illustrated below, along with a likelihood-ratio test of the same thing using sem to fit a covariance term for the residuals of the two equations.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿsysuseÿauto

.ÿ
.ÿsuregÿ(mpgÿc.weight)ÿ(headroomÿc.length),ÿnoheader

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
mpgÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿweightÿ|ÿÿÿ-.006009ÿÿÿ.0005108ÿÿÿ-11.76ÿÿÿ0.000ÿÿÿÿ-.0070102ÿÿÿ-.0050078
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ39.44121ÿÿÿ1.592028ÿÿÿÿ24.77ÿÿÿ0.000ÿÿÿÿÿ36.32089ÿÿÿÿ42.56153
-------------+----------------------------------------------------------------
headroomÿÿÿÿÿ|
ÿÿÿÿÿÿlengthÿ|ÿÿÿ.0195919ÿÿÿ.0037825ÿÿÿÿÿ5.18ÿÿÿ0.000ÿÿÿÿÿ.0121783ÿÿÿÿ.0270055
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6887166ÿÿÿ.7157624ÿÿÿÿ-0.96ÿÿÿ0.336ÿÿÿÿ-2.091585ÿÿÿÿ.7141519
------------------------------------------------------------------------------

.ÿ
.ÿ//ÿOneÿmethod,ÿquickÿandÿdirty,ÿperhaps
.ÿpredictÿdoubleÿe_mpg,ÿresidualsÿeq(#1)

.ÿpredictÿdoubleÿe_hea,ÿresidualsÿeq(#2)

.ÿpwcorrÿe_*,ÿsig

ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿe_mpgÿÿÿÿe_hea
-------------+------------------
ÿÿÿÿÿÿÿe_mpgÿ|ÿÿÿ1.0000ÿ
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿe_heaÿ|ÿÿ-0.0138ÿÿÿ1.0000ÿ
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿ0.9071
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|

.ÿ
.ÿ//ÿAlternative,ÿmaybeÿmoreÿprincipled
.ÿsemÿ(e_mpgÿ)ÿ(e_heaÿ),ÿ///
>ÿÿÿÿÿÿÿÿÿnocnsreportÿnodescribeÿnofootnoteÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ74
Estimationÿmethod:ÿml

Logÿlikelihoodÿ=ÿ-276.03339

---------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
----------------+----------------------------------------------------------------
ÿÿÿÿÿmean(e_mpg)|ÿÿÿ5.72e-14ÿÿÿ.3943236ÿÿÿÿÿ0.00ÿÿÿ1.000ÿÿÿÿÿÿ-.77286ÿÿÿÿÿÿ.77286
ÿÿÿÿÿmean(e_hea)|ÿÿ-2.80e-14ÿÿÿ.0836526ÿÿÿÿ-0.00ÿÿÿ1.000ÿÿÿÿ-.1639561ÿÿÿÿ.1639561
----------------+----------------------------------------------------------------
ÿÿÿÿÿÿvar(e_mpg)|ÿÿÿ11.50634ÿÿÿ1.891631ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ8.336823ÿÿÿÿ15.88086
ÿÿÿÿÿÿvar(e_hea)|ÿÿÿ.5178342ÿÿÿ.0851314ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3751924ÿÿÿÿÿ.714706
----------------+----------------------------------------------------------------
cov(e_mpg,e_hea)|ÿÿ-.0336703ÿÿÿÿ.283785ÿÿÿÿ-0.12ÿÿÿ0.906ÿÿÿÿ-.5898787ÿÿÿÿ.5225381
---------------------------------------------------------------------------------

.ÿestimatesÿstoreÿCovariance

.ÿ
.ÿquietlyÿsemÿ(e_mpgÿ)ÿ(e_heaÿ),ÿcovariance(e_mpg*e_hea@0)ÿ

.ÿlrtestÿCovariance

Likelihood-ratioÿtest
Assumption:ÿ.ÿnestedÿwithinÿCovariance

ÿLRÿchi2(1)ÿ=ÿÿÿ0.01
Probÿ>ÿchi2ÿ=ÿ0.9055

.ÿ
.ÿexit

endÿofÿdo-file


.

If you're that interested in some kind of null hypothesis significance test that the covariance of the residuals is exactly zero, then maybe fit a model using sem or gsem from the beginning.

Hi Joseph,

The code works well for me. Thanks alot!

[Joseph Coveney]

The code works well for me. Thanks alot!

Keep in mind that you basically did that test already when you specified the corr option back up in #1. According to the user's manual entry for the command, "corr displays the correlation matrix of the residuals between equations and performs a Breusch–Pagan test for independent equations; that is, the disturbance covariance matrix is diagonal".

[Melody Brown]

Keep in mind that you basically did that test already when you specified the corr option back up in #1. According to the user's manual entry for the command, "corr displays the correlation matrix of the residuals between equations and performs a Breusch–Pagan test for independent equations; that is, the disturbance covariance matrix is diagonal".

Got it! Thanks a lot, Joseph!