RMSEA 90% CI using Satorra-Bentler in sem CFA

[Sarah Purnell]

I am running a CFA using sem but am having trouble figuring out the output and possibly whether there is an additional command I need.
I am running a CFA using the Satorra-Bentler correction and I am not sure how to get the 90% Confidence Intervals around the RMSEA with the Satorra-Bentler correction. I am only provided the 90% confidence interval around the "Population error." Is there a specific command I need to get this output?
Thanks in advance!

[Joseph Coveney]

I am running a CFA using the Satorra-Bentler correction and I am not sure how to get the 90% Confidence Intervals around the RMSEA with the Satorra-Bentler correction. . . . Is there a specific command I need to get this output?

I'm not sure why Stata doesn't produce it, but you can calculate it manually using formulas shown here (scroll down to the bullet point named "RMSEA index" under the section titled, "Parsimony Indices") in conjunction with Stata's function for the noncentrality parameter of the noncentral chi-square distribution, npnchi2().

I show how below in a worked example (the manual calculation begins at the "Begin here" comment; the stuff above it is to create a toy dataset and fit a confirmatory factor analysis model to it for illustration).

Below that, I also show an easy, lazy method that tricks Stata into doing the calculation for you by using Mata in order to spoof the Satorra-Bentler chi-square statistic in for the conventional. See the two lines of code underneath the "Quick-and-dirty" comment. A downside is that the RSMEA and CI are still labeled in the output as "Population error", although you can see that they're for the Satorra-Bentler estimator. **Be careful with this trickster approach, because it does mess up your esimation results!** In order to avoid accidentally using the altered estimation results for anything further, I recommend manually calculating the confidence bounds instead of spoofing Stata.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ1357025618

.ÿ
.ÿtempnameÿBlockÿOffÿCorrÿMÿS

.ÿmatrixÿdefineÿ`Block'ÿ=ÿJ(3,ÿ3,ÿ0.5)ÿ+ÿI(3)ÿ*ÿ0.5

.ÿmatrixÿdefineÿ`Off'ÿ=ÿJ(3,ÿ3,ÿ0.475)

.ÿmatrixÿdefineÿ`Corr'ÿ=ÿ(`Block',ÿ`Off')ÿ\ÿ(`Off',ÿ`Block')

.ÿmatrixÿdefineÿ`M'ÿ=ÿJ(1,ÿ6,ÿ100)

.ÿmatrixÿdefineÿ`S'ÿ=ÿJ(1,ÿ6,ÿ16)

.ÿquietlyÿdrawnormÿy1ÿy2ÿy3ÿy4ÿy5ÿy6,ÿdoubleÿ///
>ÿÿÿÿÿÿÿÿÿmeans(`M')ÿsd(`S')ÿcorr(`Corr')ÿn(300)

.ÿforeachÿvarÿofÿvarlistÿ_allÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿquietlyÿreplaceÿ`var'ÿ=ÿround(`var')
ÿÿ3.ÿ}

.ÿ
.ÿsemÿ(y?ÿ<-ÿF),ÿvce(sbentler)ÿnocnsreportÿnodescribeÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ300
Estimationÿmethod:ÿml

Logÿpseudolikelihoodÿ=ÿ-7222.9632

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿSatorra–Bentler
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿy1ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ101.0833ÿÿÿ.9011384ÿÿÿ112.17ÿÿÿ0.000ÿÿÿÿÿ99.31713ÿÿÿÿ102.8495
ÿÿ-----------+----------------------------------------------------------------
ÿÿy2ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.157658ÿÿÿ.1103212ÿÿÿÿ10.49ÿÿÿ0.000ÿÿÿÿÿ.9414325ÿÿÿÿ1.373884
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.9867ÿÿÿ.9600838ÿÿÿ105.19ÿÿÿ0.000ÿÿÿÿÿ99.10494ÿÿÿÿ102.8684
ÿÿ-----------+----------------------------------------------------------------
ÿÿy3ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ.9318024ÿÿÿ.1097256ÿÿÿÿÿ8.49ÿÿÿ0.000ÿÿÿÿÿ.7167442ÿÿÿÿ1.146861
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿÿÿÿ99.83ÿÿÿ.8929448ÿÿÿ111.80ÿÿÿ0.000ÿÿÿÿÿ98.07986ÿÿÿÿ101.5801
ÿÿ-----------+----------------------------------------------------------------
ÿÿy4ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.098116ÿÿÿ.1039892ÿÿÿÿ10.56ÿÿÿ0.000ÿÿÿÿÿ.8943007ÿÿÿÿ1.301931
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.7733ÿÿÿ.8981126ÿÿÿ112.21ÿÿÿ0.000ÿÿÿÿÿ99.01306ÿÿÿÿ102.5336
ÿÿ-----------+----------------------------------------------------------------
ÿÿy5ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.006233ÿÿÿ.0999125ÿÿÿÿ10.07ÿÿÿ0.000ÿÿÿÿÿÿ.810408ÿÿÿÿ1.202058
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.3033ÿÿÿÿ.899135ÿÿÿ111.56ÿÿÿ0.000ÿÿÿÿÿ98.54106ÿÿÿÿ102.0656
ÿÿ-----------+----------------------------------------------------------------
ÿÿy6ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.063391ÿÿÿ.1039853ÿÿÿÿ10.23ÿÿÿ0.000ÿÿÿÿÿ.8595836ÿÿÿÿ1.267199
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.4733ÿÿÿ.9118616ÿÿÿ110.18ÿÿÿ0.000ÿÿÿÿÿ98.68612ÿÿÿÿ102.2605
-------------+----------------------------------------------------------------
ÿÿÿÿvar(e.y1)|ÿÿÿ136.6038ÿÿÿ11.81293ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ115.3066ÿÿÿÿ161.8345
ÿÿÿÿvar(e.y2)|ÿÿÿ133.2811ÿÿÿ13.60011ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ109.1217ÿÿÿÿ162.7893
ÿÿÿÿvar(e.y3)|ÿÿÿ146.1996ÿÿÿ13.80961ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ121.491ÿÿÿÿ175.9334
ÿÿÿÿvar(e.y4)|ÿÿÿÿ113.114ÿÿÿ10.92115ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ93.61226ÿÿÿÿ136.6784
ÿÿÿÿvar(e.y5)|ÿÿÿ134.1973ÿÿÿ12.21223ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ112.2749ÿÿÿÿ160.4002
ÿÿÿÿvar(e.y6)|ÿÿÿ128.5257ÿÿÿ12.16842ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ106.7581ÿÿÿÿ154.7317
ÿÿÿÿÿÿÿvar(F)|ÿÿÿ106.1993ÿÿÿ16.77594ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ77.92204ÿÿÿÿ144.7382
------------------------------------------------------------------------------
LRÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(9)ÿ=ÿ19.58ÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0207
Satorra–Bentlerÿscaledÿtest:ÿÿÿÿchi2(9)ÿ=ÿ20.86ÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0133

.ÿestatÿgof,ÿstats(rmseaÿindices)

----------------------------------------------------------------------------
Fitÿstatisticÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿValueÿÿÿDescription
---------------------+------------------------------------------------------
Populationÿerrorÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRMSEAÿ|ÿÿÿÿÿÿ0.063ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
ÿ90%ÿCI,ÿlowerÿboundÿ|ÿÿÿÿÿÿ0.023
ÿÿÿÿÿÿÿÿÿupperÿboundÿ|ÿÿÿÿÿÿ0.101
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿpcloseÿ|ÿÿÿÿÿÿ0.254ÿÿÿProbabilityÿRMSEAÿ<=ÿ0.05
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿSatorra–Bentlerÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿRMSEA_SBÿ|ÿÿÿÿÿÿ0.066ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
---------------------+------------------------------------------------------
Baselineÿcomparisonÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿCFIÿ|ÿÿÿÿÿÿ0.982ÿÿÿComparativeÿfitÿindex
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿTLIÿ|ÿÿÿÿÿÿ0.970ÿÿÿTucker–Lewisÿindex
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿSatorra–Bentlerÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿCFI_SBÿ|ÿÿÿÿÿÿ0.980ÿÿÿComparativeÿfitÿindex
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿTLI_SBÿ|ÿÿÿÿÿÿ0.967ÿÿÿTucker–Lewisÿindex
----------------------------------------------------------------------------

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿdisplayÿinÿsmclÿasÿtextÿ_newline(1)ÿ"Satorra-Bentlerÿ90%ÿCI,ÿlowerÿboundÿ=ÿ"ÿ///
>ÿÿÿÿÿÿÿÿÿasÿresultÿ%05.3fÿ///
>ÿÿÿÿÿÿÿÿÿsqrt(npnchi2(e(df_ms),ÿe(chi2sb_ms),ÿ0.95)ÿ/ÿ(e(N)ÿ-ÿ1)ÿ/ÿe(df_ms))

Satorra-Bentlerÿ90%ÿCI,ÿlowerÿboundÿ=ÿ0.029

.ÿdisplayÿinÿsmclÿasÿtextÿ_newline(1)ÿ"Satorra-Bentlerÿ90%ÿCI,ÿupperÿboundÿ=ÿ"ÿ///
>ÿÿÿÿÿÿÿÿÿasÿresultÿ%05.3fÿ///
>ÿÿÿÿÿÿÿÿÿsqrt(npnchi2(e(df_ms),ÿe(chi2sb_ms),ÿ0.05)ÿ/ÿ(e(N)ÿ-ÿ1)ÿ/ÿe(df_ms))

Satorra-Bentlerÿ90%ÿCI,ÿupperÿboundÿ=ÿ0.104

.ÿ
.ÿ//ÿQuick-and-dirty
.ÿmata:ÿst_numscalar("e(chi2_ms)",ÿst_numscalar("e(chi2sb_ms)"))

.ÿestatÿgof,ÿstats(rmsea)

----------------------------------------------------------------------------
Fitÿstatisticÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿValueÿÿÿDescription
---------------------+------------------------------------------------------
Populationÿerrorÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRMSEAÿ|ÿÿÿÿÿÿ0.066ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
ÿ90%ÿCI,ÿlowerÿboundÿ|ÿÿÿÿÿÿ0.029
ÿÿÿÿÿÿÿÿÿupperÿboundÿ|ÿÿÿÿÿÿ0.104
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿpcloseÿ|ÿÿÿÿÿÿ0.205ÿÿÿProbabilityÿRMSEAÿ<=ÿ0.05
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿSatorra–Bentlerÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿRMSEA_SBÿ|ÿÿÿÿÿÿ0.066ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
----------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Sarah Purnell]

Thank you so much Joseph! This worked great!

In regard to the Quick-and-dirty code, if I re-run the original sem equation prior to any further calculations, will this fix the issue of messing up estimation results for further commands?

[Sarah Purnell]

I'm not sure why Stata doesn't produce it, but you can calculate it manually using formulas shown here (scroll down to the bullet point named "RMSEA index" under the section titled, "Parsimony Indices") in conjunction with Stata's function for the noncentrality parameter of the noncentral chi-square distribution, npnchi2().

I show how below in a worked example (the manual calculation begins at the "Begin here" comment; the stuff above it is to create a toy dataset and fit a confirmatory factor analysis model to it for illustration).

Below that, I also show an easy, lazy method that tricks Stata into doing the calculation for you by using Mata in order to spoof the Satorra-Bentler chi-square statistic in for the conventional. See the two lines of code underneath the "Quick-and-dirty" comment. A downside is that the RSMEA and CI are still labeled in the output as "Population error", although you can see that they're for the Satorra-Bentler estimator. **Be careful with this trickster approach, because it does mess up your esimation results!** In order to avoid accidentally using the altered estimation results for anything further, I recommend manually calculating the confidence bounds instead of spoofing Stata.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ1357025618

.ÿ
.ÿtempnameÿBlockÿOffÿCorrÿMÿS

.ÿmatrixÿdefineÿ`Block'ÿ=ÿJ(3,ÿ3,ÿ0.5)ÿ+ÿI(3)ÿ*ÿ0.5

.ÿmatrixÿdefineÿ`Off'ÿ=ÿJ(3,ÿ3,ÿ0.475)

.ÿmatrixÿdefineÿ`Corr'ÿ=ÿ(`Block',ÿ`Off')ÿ\ÿ(`Off',ÿ`Block')

.ÿmatrixÿdefineÿ`M'ÿ=ÿJ(1,ÿ6,ÿ100)

.ÿmatrixÿdefineÿ`S'ÿ=ÿJ(1,ÿ6,ÿ16)

.ÿquietlyÿdrawnormÿy1ÿy2ÿy3ÿy4ÿy5ÿy6,ÿdoubleÿ///
>ÿÿÿÿÿÿÿÿÿmeans(`M')ÿsd(`S')ÿcorr(`Corr')ÿn(300)

.ÿforeachÿvarÿofÿvarlistÿ_allÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿquietlyÿreplaceÿ`var'ÿ=ÿround(`var')
ÿÿ3.ÿ}

.ÿ
.ÿsemÿ(y?ÿ<-ÿF),ÿvce(sbentler)ÿnocnsreportÿnodescribeÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ300
Estimationÿmethod:ÿml

Logÿpseudolikelihoodÿ=ÿ-7222.9632

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿSatorra–Bentler
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿy1ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ101.0833ÿÿÿ.9011384ÿÿÿ112.17ÿÿÿ0.000ÿÿÿÿÿ99.31713ÿÿÿÿ102.8495
ÿÿ-----------+----------------------------------------------------------------
ÿÿy2ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.157658ÿÿÿ.1103212ÿÿÿÿ10.49ÿÿÿ0.000ÿÿÿÿÿ.9414325ÿÿÿÿ1.373884
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.9867ÿÿÿ.9600838ÿÿÿ105.19ÿÿÿ0.000ÿÿÿÿÿ99.10494ÿÿÿÿ102.8684
ÿÿ-----------+----------------------------------------------------------------
ÿÿy3ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ.9318024ÿÿÿ.1097256ÿÿÿÿÿ8.49ÿÿÿ0.000ÿÿÿÿÿ.7167442ÿÿÿÿ1.146861
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿÿÿÿ99.83ÿÿÿ.8929448ÿÿÿ111.80ÿÿÿ0.000ÿÿÿÿÿ98.07986ÿÿÿÿ101.5801
ÿÿ-----------+----------------------------------------------------------------
ÿÿy4ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.098116ÿÿÿ.1039892ÿÿÿÿ10.56ÿÿÿ0.000ÿÿÿÿÿ.8943007ÿÿÿÿ1.301931
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.7733ÿÿÿ.8981126ÿÿÿ112.21ÿÿÿ0.000ÿÿÿÿÿ99.01306ÿÿÿÿ102.5336
ÿÿ-----------+----------------------------------------------------------------
ÿÿy5ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.006233ÿÿÿ.0999125ÿÿÿÿ10.07ÿÿÿ0.000ÿÿÿÿÿÿ.810408ÿÿÿÿ1.202058
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.3033ÿÿÿÿ.899135ÿÿÿ111.56ÿÿÿ0.000ÿÿÿÿÿ98.54106ÿÿÿÿ102.0656
ÿÿ-----------+----------------------------------------------------------------
ÿÿy6ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ1.063391ÿÿÿ.1039853ÿÿÿÿ10.23ÿÿÿ0.000ÿÿÿÿÿ.8595836ÿÿÿÿ1.267199
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ100.4733ÿÿÿ.9118616ÿÿÿ110.18ÿÿÿ0.000ÿÿÿÿÿ98.68612ÿÿÿÿ102.2605
-------------+----------------------------------------------------------------
ÿÿÿÿvar(e.y1)|ÿÿÿ136.6038ÿÿÿ11.81293ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ115.3066ÿÿÿÿ161.8345
ÿÿÿÿvar(e.y2)|ÿÿÿ133.2811ÿÿÿ13.60011ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ109.1217ÿÿÿÿ162.7893
ÿÿÿÿvar(e.y3)|ÿÿÿ146.1996ÿÿÿ13.80961ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ121.491ÿÿÿÿ175.9334
ÿÿÿÿvar(e.y4)|ÿÿÿÿ113.114ÿÿÿ10.92115ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ93.61226ÿÿÿÿ136.6784
ÿÿÿÿvar(e.y5)|ÿÿÿ134.1973ÿÿÿ12.21223ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ112.2749ÿÿÿÿ160.4002
ÿÿÿÿvar(e.y6)|ÿÿÿ128.5257ÿÿÿ12.16842ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ106.7581ÿÿÿÿ154.7317
ÿÿÿÿÿÿÿvar(F)|ÿÿÿ106.1993ÿÿÿ16.77594ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ77.92204ÿÿÿÿ144.7382
------------------------------------------------------------------------------
LRÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(9)ÿ=ÿ19.58ÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0207
Satorra–Bentlerÿscaledÿtest:ÿÿÿÿchi2(9)ÿ=ÿ20.86ÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0133

.ÿestatÿgof,ÿstats(rmseaÿindices)

----------------------------------------------------------------------------
Fitÿstatisticÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿValueÿÿÿDescription
---------------------+------------------------------------------------------
Populationÿerrorÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRMSEAÿ|ÿÿÿÿÿÿ0.063ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
ÿ90%ÿCI,ÿlowerÿboundÿ|ÿÿÿÿÿÿ0.023
ÿÿÿÿÿÿÿÿÿupperÿboundÿ|ÿÿÿÿÿÿ0.101
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿpcloseÿ|ÿÿÿÿÿÿ0.254ÿÿÿProbabilityÿRMSEAÿ<=ÿ0.05
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿSatorra–Bentlerÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿRMSEA_SBÿ|ÿÿÿÿÿÿ0.066ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
---------------------+------------------------------------------------------
Baselineÿcomparisonÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿCFIÿ|ÿÿÿÿÿÿ0.982ÿÿÿComparativeÿfitÿindex
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿTLIÿ|ÿÿÿÿÿÿ0.970ÿÿÿTucker–Lewisÿindex
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿSatorra–Bentlerÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿCFI_SBÿ|ÿÿÿÿÿÿ0.980ÿÿÿComparativeÿfitÿindex
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿTLI_SBÿ|ÿÿÿÿÿÿ0.967ÿÿÿTucker–Lewisÿindex
----------------------------------------------------------------------------

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿdisplayÿinÿsmclÿasÿtextÿ_newline(1)ÿ"Satorra-Bentlerÿ90%ÿCI,ÿlowerÿboundÿ=ÿ"ÿ///
>ÿÿÿÿÿÿÿÿÿasÿresultÿ%05.3fÿ///
>ÿÿÿÿÿÿÿÿÿsqrt(npnchi2(e(df_ms),ÿe(chi2sb_ms),ÿ0.95)ÿ/ÿ(e(N)ÿ-ÿ1)ÿ/ÿe(df_ms))

Satorra-Bentlerÿ90%ÿCI,ÿlowerÿboundÿ=ÿ0.029

.ÿdisplayÿinÿsmclÿasÿtextÿ_newline(1)ÿ"Satorra-Bentlerÿ90%ÿCI,ÿupperÿboundÿ=ÿ"ÿ///
>ÿÿÿÿÿÿÿÿÿasÿresultÿ%05.3fÿ///
>ÿÿÿÿÿÿÿÿÿsqrt(npnchi2(e(df_ms),ÿe(chi2sb_ms),ÿ0.05)ÿ/ÿ(e(N)ÿ-ÿ1)ÿ/ÿe(df_ms))

Satorra-Bentlerÿ90%ÿCI,ÿupperÿboundÿ=ÿ0.104

.ÿ
.ÿ//ÿQuick-and-dirty
.ÿmata:ÿst_numscalar("e(chi2_ms)",ÿst_numscalar("e(chi2sb_ms)"))

.ÿestatÿgof,ÿstats(rmsea)

----------------------------------------------------------------------------
Fitÿstatisticÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿValueÿÿÿDescription
---------------------+------------------------------------------------------
Populationÿerrorÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRMSEAÿ|ÿÿÿÿÿÿ0.066ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
ÿ90%ÿCI,ÿlowerÿboundÿ|ÿÿÿÿÿÿ0.029
ÿÿÿÿÿÿÿÿÿupperÿboundÿ|ÿÿÿÿÿÿ0.104
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿpcloseÿ|ÿÿÿÿÿÿ0.205ÿÿÿProbabilityÿRMSEAÿ<=ÿ0.05
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿSatorra–Bentlerÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿRMSEA_SBÿ|ÿÿÿÿÿÿ0.066ÿÿÿRootÿmeanÿsquaredÿerrorÿofÿapproximation
----------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

Thank you so much Joseph! This worked great!

In regard to the Quick-and-dirty code, if I re-run the original sem equation prior to any further calculations, will this fix the issue of messing up estimation results for further commands?

[Joseph Coveney]

In regard to the Quick-and-dirty code, if I re-run the original sem equation prior to any further calculations, will this fix the issue of messing up estimation results for further commands?

It should, yes.

And after re-fitting the SEM, you can verify that the "Population error" chi-square test statistic is the correct one by re-issuing the estat gof, stats(rmsea) command.