Confirmation Factor analysis with panel data

[Duong Vu]

Dear Statalist,

I am a newbie and I were stuck for some days.

I need to run CFA for a panel data which has 63 provinces from 2007 to 2015. I want to make a measurement model for the absorptive capacity of a province which constructed by six components.

I know that sem (y->x1 x2) works only for one year. And I do not know how to do with panel data.

Is it possible to use gsem (y M1[year]-> x1 x2)?

Or should I reshape the data into the wide form and run sem for each year like sem(y1->x11 x12) (y2->x21 x22)....

And is it possible if I treat the panel data as an extended cross-sectional data and use sem for it?

I really need your wisdom in this case. Please enlighten me

Thank you.

[Joseph Coveney]

I guess that this thread is the breakout from this one. It seems as if you have a single multivariate observation per province per year.

Have you had a look at what others have done? It seems popular to handle it wide, analogous to a latent growth model.

Perhaps you can account for the random effect of province by imposing an equicorrelated covariance structure on the annual latent factors, something like the first option below.

As an alternative, which would be after the user's manual example that I referred to in the previous thread, perhaps you can explicitly add the random effect for province to each equation (each year's CFA) and correspondingly constrain the latent factor covariances to zero, something like the second option below. (Convergence is much slower than the first.)

For brevity and simplicity, I've limited things to three measurements and three years in the illustration below of the two possibilities to consider. If you're comfortable with its psychometric properties—stability and invariance etc.—then your model might benefit from constraints to aid convergence, and perhaps a mean structure to aid interpretation. Others on the list might have additional (or contrary) advice.

.ÿ
.ÿversionÿ15.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1494328")'

.ÿ
.ÿ//ÿProvinces
.ÿquietlyÿsetÿobsÿ65

.ÿgenerateÿbyteÿprovinceÿ=ÿ_n

.ÿgenerateÿdoubleÿprovince_uÿ=ÿrnormal(0,ÿsqrt(2))

.ÿ
.ÿ//ÿYears
.ÿquietlyÿexpandÿ3

.ÿquietlyÿbysortÿprovince:ÿgenerateÿbyteÿyearÿ=ÿ_n

.ÿ
.ÿ//ÿMeasurementsÿwithÿerror
.ÿtempnameÿCorr

.ÿmatrixÿdefineÿ`Corr'ÿ=ÿJ(3,ÿ3,ÿ0.75)ÿ+ÿI(3)ÿ*ÿ0.25

.ÿforvaluesÿitemÿ=ÿ1/3ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿlocalÿvarlistÿ`varlist'ÿitem`item'
ÿÿ3.ÿ}

.ÿdrawnormÿ`varlist',ÿdoubleÿcorr(`Corr')

.ÿforeachÿvarÿofÿvarlistÿ`varlist'ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿquietlyÿreplaceÿ`var'ÿ=ÿprovince_uÿ+ÿ`var'
ÿÿ3.ÿ}

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿquietlyÿreshapeÿwideÿitem?,ÿi(province)ÿj(year)

.ÿ
.ÿ//ÿFirstÿapproach
.ÿforvaluesÿyearÿ=ÿ1/3ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿlocalÿmodelÿ`model'ÿ(item?`year'ÿ<-ÿAC`year')
ÿÿ3.ÿ}

.ÿ
.ÿforvaluesÿyearÿ=ÿ1/2ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿforvaluesÿnext_yearÿ=ÿ`=`year'ÿ+ÿ1'/3ÿ{
ÿÿ3.ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlocalÿcovarianceÿ`covariance'ÿAC`year'*AC`next_year'@c1
ÿÿ4.ÿÿÿÿÿÿÿÿÿ}
ÿÿ5.ÿ}

.ÿ
.ÿsemÿ`model',ÿcovariance(`covariance')ÿnocnsreportÿnodescribeÿnofootnoteÿÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿ65
Estimationÿmethodÿÿ=ÿml
Logÿlikelihoodÿÿÿÿÿ=ÿ-705.54588

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿitem11ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC1ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.5274207ÿÿÿÿ.201514ÿÿÿÿ-2.62ÿÿÿ0.009ÿÿÿÿ-.9223809ÿÿÿ-.1324605
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem21ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC1ÿ|ÿÿÿ.9831336ÿÿÿÿ.061192ÿÿÿÿ16.07ÿÿÿ0.000ÿÿÿÿÿ.8631995ÿÿÿÿ1.103068
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4436036ÿÿÿ.1938397ÿÿÿÿ-2.29ÿÿÿ0.022ÿÿÿÿ-.8235224ÿÿÿ-.0636849
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem31ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC1ÿ|ÿÿÿ.9752267ÿÿÿ.0591238ÿÿÿÿ16.49ÿÿÿ0.000ÿÿÿÿÿ.8593462ÿÿÿÿ1.091107
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6352514ÿÿÿ.1914424ÿÿÿÿ-3.32ÿÿÿ0.001ÿÿÿÿ-1.010471ÿÿÿ-.2600312
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem12ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC2ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.7064861ÿÿÿ.2066509ÿÿÿÿ-3.42ÿÿÿ0.001ÿÿÿÿ-1.111514ÿÿÿ-.3014577
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem22ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC2ÿ|ÿÿÿ.9843264ÿÿÿ.0541768ÿÿÿÿ18.17ÿÿÿ0.000ÿÿÿÿÿ.8781417ÿÿÿÿ1.090511
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.5480426ÿÿÿ.2019035ÿÿÿÿ-2.71ÿÿÿ0.007ÿÿÿÿ-.9437662ÿÿÿ-.1523191
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem32ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC2ÿ|ÿÿÿ.9672261ÿÿÿ.0549762ÿÿÿÿ17.59ÿÿÿ0.000ÿÿÿÿÿ.8594748ÿÿÿÿ1.074977
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6303917ÿÿÿ.1999448ÿÿÿÿ-3.15ÿÿÿ0.002ÿÿÿÿ-1.022276ÿÿÿ-.2385071
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem13ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC3ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.1810775ÿÿÿ.2084531ÿÿÿÿ-0.87ÿÿÿ0.385ÿÿÿÿ-.5896381ÿÿÿÿÿ.227483
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem23ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC3ÿ|ÿÿÿ.9239949ÿÿÿ.0534575ÿÿÿÿ17.28ÿÿÿ0.000ÿÿÿÿÿ.8192202ÿÿÿÿÿ1.02877
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3242394ÿÿÿÿ.195048ÿÿÿÿ-1.66ÿÿÿ0.096ÿÿÿÿ-.7065264ÿÿÿÿ.0580476
ÿÿ-----------+----------------------------------------------------------------
ÿÿitem33ÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿAC3ÿ|ÿÿÿ.9187966ÿÿÿÿ.054129ÿÿÿÿ16.97ÿÿÿ0.000ÿÿÿÿÿ.8127058ÿÿÿÿ1.024887
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4154144ÿÿÿ.1946614ÿÿÿÿ-2.13ÿÿÿ0.033ÿÿÿÿ-.7969437ÿÿÿ-.0338852
-------------+----------------------------------------------------------------
var(e.item11)|ÿÿÿ.3393043ÿÿÿ.0783851ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2157482ÿÿÿÿ.5336193
var(e.item21)|ÿÿÿ.2190279ÿÿÿ.0628846ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1247708ÿÿÿÿ.3844909
var(e.item31)|ÿÿÿ.1946086ÿÿÿ.0589427ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.107486ÿÿÿÿ.3523485
var(e.item12)|ÿÿÿ.2634809ÿÿÿ.0696836ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1569024ÿÿÿÿ.4424548
var(e.item22)|ÿÿÿ.2155448ÿÿÿ.0623448ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1222738ÿÿÿÿ.3799633
var(e.item32)|ÿÿÿ.2482253ÿÿÿ.0643393ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1493541ÿÿÿÿ.4125484
var(e.item13)|ÿÿÿ.2279364ÿÿÿÿ.068704ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1262545ÿÿÿÿ.4115101
var(e.item23)|ÿÿÿ.2560458ÿÿÿÿ.066518ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1538808ÿÿÿÿ.4260404
var(e.item33)|ÿÿÿ.2711254ÿÿÿ.0681879ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1656126ÿÿÿÿ.4438609
ÿÿÿÿÿvar(AC1)|ÿÿÿ2.300209ÿÿÿ.4183781ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.610441ÿÿÿÿ3.285411
ÿÿÿÿÿvar(AC2)|ÿÿÿ2.512319ÿÿÿ.4162342ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.815725ÿÿÿÿ3.476158
ÿÿÿÿÿvar(AC3)|ÿÿÿ2.596489ÿÿÿ.4296265ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.87734ÿÿÿÿ3.591121
-------------+----------------------------------------------------------------
ÿcov(AC1,AC2)|ÿÿÿ1.710901ÿÿÿÿ.358309ÿÿÿÿÿ4.77ÿÿÿ0.000ÿÿÿÿÿ1.008629ÿÿÿÿ2.413174
ÿcov(AC1,AC3)|ÿÿÿ1.710901ÿÿÿÿ.358309ÿÿÿÿÿ4.77ÿÿÿ0.000ÿÿÿÿÿ1.008629ÿÿÿÿ2.413174
ÿcov(AC2,AC3)|ÿÿÿ1.710901ÿÿÿÿ.358309ÿÿÿÿÿ4.77ÿÿÿ0.000ÿÿÿÿÿ1.008629ÿÿÿÿ2.413174
------------------------------------------------------------------------------

.ÿ
.ÿ//ÿSecondÿapproach
.ÿmacroÿdropÿ_all

.ÿforvaluesÿyearÿ=ÿ1/3ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿlocalÿmodelÿ`model'ÿ(item?`year'ÿ<-ÿAC`year'ÿM[province])
ÿÿ3.ÿ}

.ÿ
.ÿforvaluesÿyearÿ=ÿ1/2ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿforvaluesÿnext_yearÿ=ÿ`=`year'ÿ+ÿ1'/3ÿ{
ÿÿ3.ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlocalÿcovarianceÿ`covariance'ÿAC`year'*AC`next_year'@0
ÿÿ4.ÿÿÿÿÿÿÿÿÿ}
ÿÿ5.ÿ}

.ÿ
.ÿgsemÿ`model',ÿcovariance(`covariance')ÿintmethod(laplace)ÿdifficultÿnocnsreportÿnodvheaderÿnolog

GeneralizedÿstructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿ65
Logÿlikelihoodÿ=ÿ-704.37277

----------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------+----------------------------------------------------------------
item11ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC1ÿ|ÿÿÿ1.114752ÿÿÿ.1807058ÿÿÿÿÿ6.17ÿÿÿ0.000ÿÿÿÿÿ.7605748ÿÿÿÿ1.468929
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.5274207ÿÿÿ.1969235ÿÿÿÿ-2.68ÿÿÿ0.007ÿÿÿÿ-.9133838ÿÿÿ-.1414576
-----------------+----------------------------------------------------------------
item21ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.029823ÿÿÿ.0878315ÿÿÿÿ11.72ÿÿÿ0.000ÿÿÿÿÿ.8576768ÿÿÿÿÿ1.20197
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC1ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4436036ÿÿÿ.1909239ÿÿÿÿ-2.32ÿÿÿ0.020ÿÿÿÿ-.8178077ÿÿÿ-.0693996
-----------------+----------------------------------------------------------------
item31ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ.9954368ÿÿÿ.0830593ÿÿÿÿ11.98ÿÿÿ0.000ÿÿÿÿÿ.8326436ÿÿÿÿÿ1.15823
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC1ÿ|ÿÿÿ1.076055ÿÿÿ.1624367ÿÿÿÿÿ6.62ÿÿÿ0.000ÿÿÿÿÿÿ.757685ÿÿÿÿ1.394425
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6352514ÿÿÿ.1885372ÿÿÿÿ-3.37ÿÿÿ0.001ÿÿÿÿ-1.004777ÿÿÿ-.2657253
-----------------+----------------------------------------------------------------
item12ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.139621ÿÿÿ.1910121ÿÿÿÿÿ5.97ÿÿÿ0.000ÿÿÿÿÿ.7652443ÿÿÿÿ1.513998
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC2ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.7064861ÿÿÿ.2120341ÿÿÿÿ-3.33ÿÿÿ0.001ÿÿÿÿ-1.122065ÿÿÿ-.2909069
-----------------+----------------------------------------------------------------
item22ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.114758ÿÿÿ.1875219ÿÿÿÿÿ5.94ÿÿÿ0.000ÿÿÿÿÿÿ.747222ÿÿÿÿ1.482294
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC2ÿ|ÿÿÿ.9747296ÿÿÿ.1375899ÿÿÿÿÿ7.08ÿÿÿ0.000ÿÿÿÿÿ.7050584ÿÿÿÿ1.244401
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.5480426ÿÿÿ.2059332ÿÿÿÿ-2.66ÿÿÿ0.008ÿÿÿÿ-.9516642ÿÿÿ-.1444211
-----------------+----------------------------------------------------------------
item32ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.060217ÿÿÿ.1819919ÿÿÿÿÿ5.83ÿÿÿ0.000ÿÿÿÿÿ.7035196ÿÿÿÿ1.416915
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC2ÿ|ÿÿÿ1.050839ÿÿÿÿ.153482ÿÿÿÿÿ6.85ÿÿÿ0.000ÿÿÿÿÿ.7500202ÿÿÿÿ1.351659
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6303917ÿÿÿ.2038744ÿÿÿÿ-3.09ÿÿÿ0.002ÿÿÿÿ-1.029978ÿÿÿ-.2308053
-----------------+----------------------------------------------------------------
item13ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.056274ÿÿÿ.1816768ÿÿÿÿÿ5.81ÿÿÿ0.000ÿÿÿÿÿ.7001945ÿÿÿÿ1.412354
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC3ÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.1810775ÿÿÿ.2080606ÿÿÿÿ-0.87ÿÿÿ0.384ÿÿÿÿ-.5888688ÿÿÿÿ.2267137
-----------------+----------------------------------------------------------------
item23ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.008584ÿÿÿ.1685453ÿÿÿÿÿ5.98ÿÿÿ0.000ÿÿÿÿÿ.6782414ÿÿÿÿ1.338927
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC3ÿ|ÿÿÿ.8497558ÿÿÿ.1161281ÿÿÿÿÿ7.32ÿÿÿ0.000ÿÿÿÿÿ.6221489ÿÿÿÿ1.077363
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3242394ÿÿÿ.1947632ÿÿÿÿ-1.66ÿÿÿ0.096ÿÿÿÿ-.7059682ÿÿÿÿ.0574894
-----------------+----------------------------------------------------------------
item33ÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿM[province]ÿ|ÿÿÿ1.007719ÿÿÿ.1704205ÿÿÿÿÿ5.91ÿÿÿ0.000ÿÿÿÿÿ.6737012ÿÿÿÿ1.341737
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿAC3ÿ|ÿÿÿ.8365211ÿÿÿÿ.116352ÿÿÿÿÿ7.19ÿÿÿ0.000ÿÿÿÿÿ.6084754ÿÿÿÿ1.064567
ÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4154144ÿÿÿ.1943792ÿÿÿÿ-2.14ÿÿÿ0.033ÿÿÿÿ-.7963907ÿÿÿ-.0344382
-----------------+----------------------------------------------------------------
ÿvar(M[province])|ÿÿÿ1.489091ÿÿÿ.4420499ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.832213ÿÿÿÿ2.664452
ÿÿÿÿÿÿÿÿÿvar(AC1)|ÿÿÿ.5620171ÿÿÿ.2204227ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2605607ÿÿÿÿ1.212244
ÿÿÿÿÿÿÿÿÿvar(AC2)|ÿÿÿ.7212933ÿÿÿÿ.279169ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3378028ÿÿÿÿ1.540141
ÿÿÿÿÿÿÿÿÿvar(AC3)|ÿÿÿ.9502176ÿÿÿ.2890026ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.5235228ÿÿÿÿ1.724688
-----------------+----------------------------------------------------------------
ÿÿÿÿvar(e.item11)|ÿÿÿÿ.333134ÿÿÿ.0827353ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2047478ÿÿÿÿ.5420241
ÿÿÿÿvar(e.item21)|ÿÿÿ.2281243ÿÿÿ.0622322ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1336486ÿÿÿÿ.3893847
ÿÿÿÿvar(e.item31)|ÿÿÿ.1842193ÿÿÿ.0630057ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0942349ÿÿÿÿ.3601293
ÿÿÿÿvar(e.item12)|ÿÿÿ.2670703ÿÿÿÿ.069367ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1605241ÿÿÿÿ.4443354
ÿÿÿÿvar(e.item22)|ÿÿÿ.2207789ÿÿÿÿ.062196ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1271055ÿÿÿÿ.3834874
ÿÿÿÿvar(e.item32)|ÿÿÿ.2313833ÿÿÿ.0704065ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1274453ÿÿÿÿ.4200878
ÿÿÿÿvar(e.item13)|ÿÿÿ.2021788ÿÿÿ.0777882ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0951121ÿÿÿÿ.4297691
ÿÿÿÿvar(e.item23)|ÿÿÿ.2647222ÿÿÿ.0678969ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1601294ÿÿÿÿ.4376325
ÿÿÿÿvar(e.item33)|ÿÿÿÿ.278813ÿÿÿ.0687162ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1719991ÿÿÿÿ.4519599
----------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Duong Vu]

Hi, Joseph Coveney,

Thank you very much for your guidance. I will try to play around with this

[Joseph Coveney]

Thank you very much for your guidance. I will try to play around with this

You can see that the two models are just different parameterizations of the same structural equation model (they have the same log likelihood, same factor loadings, same intercepts etc.) The two parameterizations of the SEM are directly analogous to expressing a variance component model either as a repeated measures model with compound symmetric covariance structure on the residuals or as a random effects model.

.ÿ
.ÿversionÿ15.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿwebuseÿpig
(Longitudinalÿanalysisÿofÿpigÿweights)

.ÿ
.ÿ//ÿAnalogueÿofÿfirstÿoption
.ÿmixedÿweightÿi.weekÿ||ÿid:ÿ,ÿnoconstantÿresiduals(exchangeable)ÿ///
>ÿÿÿÿÿÿÿÿÿremlÿdfmethod(satterthwaite)ÿnolrtestÿnolog

Mixed-effectsÿREMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ432
Groupÿvariable:ÿidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ48

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ9
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ9.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ9
DFÿmethod:ÿSatterthwaiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDF:ÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿ72.24
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿ342.25
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿ376.00

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿF(8,ÿÿÿ376.00)ÿÿÿÿ=ÿÿÿÿ3232.75
Logÿrestricted-likelihoodÿ=ÿ-1007.9601ÿÿÿÿÿÿÿÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000

------------------------------------------------------------------------------
ÿÿÿÿÿÿweightÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿweekÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿÿ6.760417ÿÿÿ.4231323ÿÿÿÿ15.98ÿÿÿ0.000ÿÿÿÿÿ5.928415ÿÿÿÿ7.592419
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿÿ13.84375ÿÿÿ.4231323ÿÿÿÿ32.72ÿÿÿ0.000ÿÿÿÿÿ13.01175ÿÿÿÿ14.67575
ÿÿÿÿÿÿÿÿÿÿ4ÿÿ|ÿÿÿÿÿ19.375ÿÿÿ.4231323ÿÿÿÿ45.79ÿÿÿ0.000ÿÿÿÿÿÿÿ18.543ÿÿÿÿÿÿ20.207
ÿÿÿÿÿÿÿÿÿÿ5ÿÿ|ÿÿÿ25.13542ÿÿÿ.4231323ÿÿÿÿ59.40ÿÿÿ0.000ÿÿÿÿÿ24.30341ÿÿÿÿ25.96742
ÿÿÿÿÿÿÿÿÿÿ6ÿÿ|ÿÿÿ31.42708ÿÿÿ.4231323ÿÿÿÿ74.27ÿÿÿ0.000ÿÿÿÿÿ30.59508ÿÿÿÿ32.25909
ÿÿÿÿÿÿÿÿÿÿ7ÿÿ|ÿÿÿÿ37.4375ÿÿÿ.4231323ÿÿÿÿ88.48ÿÿÿ0.000ÿÿÿÿÿÿ36.6055ÿÿÿÿÿ38.2695
ÿÿÿÿÿÿÿÿÿÿ8ÿÿ|ÿÿÿ44.28125ÿÿÿ.4231323ÿÿÿ104.65ÿÿÿ0.000ÿÿÿÿÿ43.44925ÿÿÿÿ45.11325
ÿÿÿÿÿÿÿÿÿÿ9ÿÿ|ÿÿÿ50.19792ÿÿÿ.4231323ÿÿÿ118.63ÿÿÿ0.000ÿÿÿÿÿ49.36591ÿÿÿÿ51.02992
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ25.02083ÿÿÿ.6365548ÿÿÿÿ39.31ÿÿÿ0.000ÿÿÿÿÿ23.75196ÿÿÿÿ26.28971
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿParametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿErr.ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------------------+------------------------------------------------
id:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(empty)ÿ|
-----------------------------+------------------------------------------------
Residual:ÿExchangeableÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(e)ÿ|ÿÿÿÿ19.4497ÿÿÿ3.236267ÿÿÿÿÿÿ14.03718ÿÿÿÿ26.94919
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcov(e)ÿ|ÿÿÿ15.15271ÿÿÿ3.224444ÿÿÿÿÿÿÿ8.83292ÿÿÿÿ21.47251
------------------------------------------------------------------------------

.ÿ
.ÿ//ÿAnalogueÿofÿsecondÿoption
.ÿmixedÿweightÿi.weekÿ||ÿid:ÿ,ÿremlÿdfmethod(satterthwaite)ÿnolrtestÿnolog

Mixed-effectsÿREMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ432
Groupÿvariable:ÿidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ48

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ9
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ9.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ9
DFÿmethod:ÿSatterthwaiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDF:ÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿ72.24
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿ342.25
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿ376.00

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿF(8,ÿÿÿ376.00)ÿÿÿÿ=ÿÿÿÿ3232.74
Logÿrestricted-likelihoodÿ=ÿ-1007.9601ÿÿÿÿÿÿÿÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000

------------------------------------------------------------------------------
ÿÿÿÿÿÿweightÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿweekÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿÿ6.760417ÿÿÿ.4231323ÿÿÿÿ15.98ÿÿÿ0.000ÿÿÿÿÿ5.928414ÿÿÿÿ7.592419
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿÿ13.84375ÿÿÿ.4231323ÿÿÿÿ32.72ÿÿÿ0.000ÿÿÿÿÿ13.01175ÿÿÿÿ14.67575
ÿÿÿÿÿÿÿÿÿÿ4ÿÿ|ÿÿÿÿÿ19.375ÿÿÿ.4231323ÿÿÿÿ45.79ÿÿÿ0.000ÿÿÿÿÿÿÿ18.543ÿÿÿÿÿÿ20.207
ÿÿÿÿÿÿÿÿÿÿ5ÿÿ|ÿÿÿ25.13542ÿÿÿ.4231323ÿÿÿÿ59.40ÿÿÿ0.000ÿÿÿÿÿ24.30341ÿÿÿÿ25.96742
ÿÿÿÿÿÿÿÿÿÿ6ÿÿ|ÿÿÿ31.42708ÿÿÿ.4231323ÿÿÿÿ74.27ÿÿÿ0.000ÿÿÿÿÿ30.59508ÿÿÿÿ32.25909
ÿÿÿÿÿÿÿÿÿÿ7ÿÿ|ÿÿÿÿ37.4375ÿÿÿ.4231323ÿÿÿÿ88.48ÿÿÿ0.000ÿÿÿÿÿÿ36.6055ÿÿÿÿÿ38.2695
ÿÿÿÿÿÿÿÿÿÿ8ÿÿ|ÿÿÿ44.28125ÿÿÿ.4231323ÿÿÿ104.65ÿÿÿ0.000ÿÿÿÿÿ43.44925ÿÿÿÿ45.11325
ÿÿÿÿÿÿÿÿÿÿ9ÿÿ|ÿÿÿ50.19792ÿÿÿ.4231323ÿÿÿ118.63ÿÿÿ0.000ÿÿÿÿÿ49.36591ÿÿÿÿ51.02992
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ25.02083ÿÿÿ.6365548ÿÿÿÿ39.31ÿÿÿ0.000ÿÿÿÿÿ23.75196ÿÿÿÿ26.28971
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿParametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿErr.ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------------------+------------------------------------------------
id:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ15.15271ÿÿÿ3.224443ÿÿÿÿÿÿ9.985222ÿÿÿÿ22.99445
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ4.296983ÿÿÿ.3133897ÿÿÿÿÿÿ3.724632ÿÿÿÿ4.957285
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Duong Vu]

Hi Joseph Coveney,

I used the first method which is kind of repeat the measurement in 2007, 2011 and 2015.
However, I have one problem which when I standardized the coefficients, the correlation between AC2011 and AC2015 is more than 1. I think it should not be that way but I could not find a reason. Additionally, my SRMR is 0.114 which is more than 0.08

Would you mind giving me some advice?

Thank you

[Joseph Coveney]

I never standardize coefficients and I don't do fit statistics, so I'm afraid that I don't have any advice for you, sorry.