Second-order factor analysis

[Andrea Toledo]

Dear StataListers,

I am working on a project on which I am trying to estimate a factor analysis using 9 dummies variables.
On a first step I estimated a first order confirmatory factor analysis, and I didn't have problems but when I tries to estimate
a second order confirmatory factor analysis, the model runs and runs and runs and gives me the message that iterations are "not concave".
Because of all the variables have two categories, I use the method adf (asympotically distribution free),
but I also tried to estimate the model using the method (ml) combined with option vce (robust) and with vce (bootstrap). I have the same problem

My question is the following: what does this "not concave" message mean? What should I do?

My code:

(1) FIRST ORDER CONFIRMATORY FACTOR ANALYSIS

sem (Ayudaeconomica -> coberturamedica ITICBT ayudaexterna ,)
(Zonaubicacion -> basural zonainundable villaemergencia,)
(Infraestructura -> baño pisos techointerior hacinamiento),
latent (Ayudaeconomica Zonaubicacion Infraestructura) method(adf)

(2) SECOND ORDER CONFIRMATORY FACTOR ANALYSIS

sem (Incapacidadeconomica -> coberturamedica ITICBT ayudaexterna ,)
(Zonaubicacion -> basural zonainundable villaemergencia,)
(Infraestructura -> baño pisos techointerior hacinamiento,)
(Pobrezamultidimensional -> Infraestructura Incapacidadeconomica Zonaubicacion ),
latent (Pobrezamultidimensional Incapacidadeconomica Zonaubicacion Infraestructura)
method(adf) iterate ( 100 )

RESULTS
Endogenous variables

Measurement: coberturamedica ITICBT ayudaexterna basural zonainundable villaemergencia baño pisos techointerior hacinamiento
Latent: Incapacidadeconomica Zonaubicacion Infraestructura

Exogenous variables
Latent: Pobrezamultidimensional

Fitting baseline model:

Iteration 0: discrepancy = .43060013
Iteration 1: discrepancy = .28040098
Iteration 2: discrepancy = .28040098

Fitting target model:
Iteration 0: discrepancy = 11.835502 (not concave)
Iteration 1: discrepancy = 1.3103552 (not concave)
Iteration 2: discrepancy = .07200014 (not concave)
Iteration 3: discrepancy = .06590574 (not concave)
Iteration 4: discrepancy = .06213892 (not concave)
Iteration 5: discrepancy = .06168234 (not concave)
Iteration 6: discrepancy = .06140415 (not concave)
Iteration 7: discrepancy = .06100357 (not concave)
Iteration 8: discrepancy = .06040023 (not concave)
Iteration 9: discrepancy = .06021822 (not concave)
Iteration 10: discrepancy = .05955194 (not concave)
Iteration 11: discrepancy = .0594336 (not concave)
Iteration 12: discrepancy = .05862482 (not concave)
Iteration 13: discrepancy = .0575207 (not concave)
Iteration 14: discrepancy = .05601082 (not concave)
Iteration 15: discrepancy = .05516756 (not concave)
Iteration 16: discrepancy = .05490172 (not concave)
Iteration 17: discrepancy = .05486508 (not concave)
Iteration 18: discrepancy = .05484651 (not concave)
Iteration 19: discrepancy = .05484535 (not concave)
Iteration 20: discrepancy = .05484476 (not concave)
Iteration 21: discrepancy = .05484462 (not concave)
.
.
.
.
Iteration 98: discrepancy = .05484455 (not concave)
Iteration 99: discrepancy = .05484455 (not concave)
Iteration 100: discrepancy = .05484455 (not concave)
convergence not achieved

Structural equation model

Number of obs = 15,254
Estimation method = adf
Discrepancy = .05484455

[Joseph Coveney]

Sometimes it helps to model covariances between the first-order latent factors instead of modeling a second-order variance. Try something like the following and see whether it converges.

sem ///
    (coberturamedica ITICBT ayudaexterna <- Incapacidadeconomica) ///
    (basural zonainundable villaemergencia <- Zonaubicacion) ///
    (baño pisos techointerior hacinamiento <- Infraestructura), ///
        latent(Incapacidadeconomica Zonaubicacion Infraestructura) ///
        covariance(Incapacidadeconomica*Zonaubicacion ///
            Incapacidadeconomica*Infraestructura ///
            Zonaubicacion*Infraestructura) ///
        method(adf)

[Andrea Toledo]

Dear Joseph, if I do these, my model converges. Thank you so much
But I have a problem. In my model, I need estimated the variable Pobrezamultidimensional. So, if a second-order confirmatory factor analysis doesn't work, what I should do ?

[Joseph Coveney]

The two models are equivalent, and so you can use the fitted values from the model that converges as constraints for the second-order CFA in order to allow it to converge. You probably don't need to constrain all of the parameter estimates to the fitted values, but rather only those that are having trouble, which are probably the three variances of the first-order factors. So try constraining those three parameter estimates first.

I illustrate the method below using a fake dataset. For convenience in the illustration, instead of using the asymptotically distribution-free method, I use the tetrachoric correlation matrix of the manifest binary variables and use -sem- with summary statistics in a separate frame. Begin at the "Begin here" comment in the output below; the first part of the output just shows making of the fake dataset.. (I shorten the names of the manifest and latent variables for brevity, and I use only lower-case variable names for manifest variables.)

I first show that the second-order CFA fails to converge (which is your problem). Then show that the equivalent model with three covariances (instead of two factor loadings and one second-order latent variable's variance) does converge, which is also what you observe with your dataset. Then I take the fitted values of the three sensitive parameter estimates (the variances of the three first-order latent factors) and use them to constrain the corresponding variances in the second-order CFA, and voilà. (Each step of the process is marked with a // comment so that you can more easily follow what's going on.)

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1637544")'

.ÿ
.ÿquietlyÿsetÿobsÿ15254

.ÿ
.ÿquietlyÿdrawnormÿcoberturamedicaÿITICBTÿayudaexterna,ÿdoubleÿ///
>ÿÿÿÿÿÿÿÿÿcorr(1ÿ0.5ÿ0.5ÿ\ÿ0.5ÿ1ÿ0.5ÿ\ÿ0.5ÿ0.5ÿ1)

.ÿ
.ÿquietlyÿdrawnormÿbasuralÿzonainundableÿvillaemergencia,ÿdoubleÿ///
>ÿÿÿÿÿÿÿÿÿcorr(1ÿ0.5ÿ0.5ÿ\ÿ0.5ÿ1ÿ0.5ÿ\ÿ0.5ÿ0.5ÿ1)

.ÿ
.ÿquietlyÿdrawnormÿbanoÿpisosÿtechointeriorÿhacinamiento,ÿdoubleÿ///
>ÿÿÿÿÿÿÿÿÿcorr(1ÿ0.5ÿ0.5ÿ0.5ÿ\ÿ0.5ÿ1ÿ0.5ÿ0.5ÿ\ÿ0.5ÿ0.5ÿ1ÿ0.5ÿ\ÿ0.5ÿ0.5ÿ0.5ÿ1)

.ÿ
.ÿgenerateÿdoubleÿcommonÿ=ÿrnormal()

.ÿ
.ÿlocalÿvarlist

.ÿforeachÿvarÿofÿvarlistÿ_allÿ{
ÿÿ2.ÿ
.ÿÿÿÿÿÿÿÿÿifÿ"`var'"ÿ!=ÿ"common"ÿ{
ÿÿ3.ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿquietlyÿreplaceÿ`var'ÿ=ÿ(`var'ÿ+ÿcommon)ÿ>ÿ0
ÿÿ4.ÿ
.ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlocalÿnewÿ=ÿstrlower(substr("`var'",ÿ1,ÿ3))
ÿÿ5.ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿrenameÿ`var'ÿ`new'
ÿÿ6.ÿ
.ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlocalÿvarlistÿ`varlist'ÿ`new'
ÿÿ7.ÿÿÿÿÿÿÿÿÿ}
ÿÿ8.ÿ}

.ÿdropÿcommon

.ÿ
.ÿquietlyÿtetrachoricÿ_all

.ÿtempnameÿRho

.ÿmatrixÿdefineÿ`Rho'ÿ=ÿr(Rho)

.ÿframeÿcreateÿSSD

.ÿframeÿSSDÿ{
.ÿÿÿÿÿÿÿÿÿquietlyÿssdÿinitÿ`varlist'
.ÿÿÿÿÿÿÿÿÿquietlyÿssdÿsetÿobsÿ`r(N)'
.ÿÿÿÿÿÿÿÿÿquietlyÿssdÿsetÿcovariancesÿ(stata)ÿ`Rho'
.ÿ}

.ÿcwfÿSSD

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿ//ÿDemonstratesÿthatÿsecond-orderÿCFAÿwon'tÿconverge
.ÿsemÿ///
>ÿÿÿÿÿÿÿÿÿ(cobÿitiÿayuÿ<-ÿInc)ÿ///
>ÿÿÿÿÿÿÿÿÿ(basÿzonÿvilÿ<-ÿZon)ÿ///
>ÿÿÿÿÿÿÿÿÿ(banÿpisÿtecÿhacÿ<-ÿInf)ÿ///
>ÿÿÿÿÿÿÿÿÿ(IncÿZonÿInfÿ<-ÿPob),ÿiterate(10)ÿnocnsreportÿnodescribe

Fittingÿtargetÿmodel:
Iterationÿ0:ÿÿÿlogÿlikelihoodÿ=ÿ-167604.39ÿÿ(notÿconcave)
Iterationÿ1:ÿÿÿlogÿlikelihoodÿ=ÿ-166014.25ÿÿ(notÿconcave)
Iterationÿ2:ÿÿÿlogÿlikelihoodÿ=ÿ-162506.63ÿÿ(notÿconcave)
Iterationÿ3:ÿÿÿlogÿlikelihoodÿ=ÿ-161810.35ÿÿ(notÿconcave)
Iterationÿ4:ÿÿÿlogÿlikelihoodÿ=ÿ-161256.49ÿÿ
Iterationÿ5:ÿÿÿlogÿlikelihoodÿ=ÿ-161049.91ÿÿ(backedÿup)
Iterationÿ6:ÿÿÿlogÿlikelihoodÿ=ÿÿ-161044.6ÿÿ(backedÿup)
Iterationÿ7:ÿÿÿlogÿlikelihoodÿ=ÿ-161043.95ÿÿ(backedÿup)
Iterationÿ8:ÿÿÿlogÿlikelihoodÿ=ÿ-161043.62ÿÿ(backedÿup)
Iterationÿ9:ÿÿÿlogÿlikelihoodÿ=ÿ-161043.46ÿÿ(backedÿup)
Iterationÿ10:ÿÿlogÿlikelihoodÿ=ÿ-161043.42ÿÿ(backedÿup)
convergenceÿnotÿachieved

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ15,254
Estimationÿmethod:ÿml

Logÿlikelihoodÿ=ÿ-161043.42

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
Structuralÿÿÿ|
ÿÿIncÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿPobÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿZonÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿPobÿ|ÿÿÿ.3404844ÿÿÿ.0103168ÿÿÿÿ33.00ÿÿÿ0.000ÿÿÿÿÿ.3202638ÿÿÿÿ.3607051
ÿÿ-----------+----------------------------------------------------------------
ÿÿInfÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿPobÿ|ÿÿÿ.3388309ÿÿÿ.0102503ÿÿÿÿ33.06ÿÿÿ0.000ÿÿÿÿÿ.3187406ÿÿÿÿ.3589213
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿcobÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿitiÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.9938629ÿÿÿ.0076618ÿÿÿ129.72ÿÿÿ0.000ÿÿÿÿÿÿ.978846ÿÿÿÿÿ1.00888
ÿÿ-----------+----------------------------------------------------------------
ÿÿayuÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.9844135ÿÿÿ.0076637ÿÿÿ128.45ÿÿÿ0.000ÿÿÿÿÿ.9693929ÿÿÿÿ.9994341
ÿÿ-----------+----------------------------------------------------------------
ÿÿbasÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿzonÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ1.002529ÿÿÿÿ.008183ÿÿÿ122.51ÿÿÿ0.000ÿÿÿÿÿ.9864902ÿÿÿÿ1.018567
ÿÿ-----------+----------------------------------------------------------------
ÿÿvilÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ.9940628ÿÿÿÿ.008137ÿÿÿ122.17ÿÿÿ0.000ÿÿÿÿÿ.9781145ÿÿÿÿ1.010011
ÿÿ-----------+----------------------------------------------------------------
ÿÿbanÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿpisÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ.9901335ÿÿÿ.0081137ÿÿÿ122.03ÿÿÿ0.000ÿÿÿÿÿ.9742309ÿÿÿÿ1.006036
ÿÿ-----------+----------------------------------------------------------------
ÿÿtecÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ1.002295ÿÿÿ.0081095ÿÿÿ123.59ÿÿÿ0.000ÿÿÿÿÿ.9864008ÿÿÿÿÿ1.01819
ÿÿ-----------+----------------------------------------------------------------
ÿÿhacÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ1.000431ÿÿÿ.0081067ÿÿÿ123.41ÿÿÿ0.000ÿÿÿÿÿ.9845419ÿÿÿÿÿ1.01632
-------------+----------------------------------------------------------------
ÿÿÿvar(e.cob)|ÿÿÿ.2304032ÿÿÿÿ.004275ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2221748ÿÿÿÿ.2389363
ÿÿÿvar(e.iti)|ÿÿÿÿ.235178ÿÿÿÿ.004204ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2270811ÿÿÿÿ.2435636
ÿÿÿvar(e.ayu)|ÿÿÿ.2499208ÿÿÿ.0042726ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2416854ÿÿÿÿ.2584368
ÿÿÿvar(e.bas)|ÿÿÿ.2445579ÿÿÿ.0045219ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2358537ÿÿÿÿ.2535832
ÿÿÿvar(e.zon)|ÿÿÿ.2428445ÿÿÿ.0044387ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2342987ÿÿÿÿÿ.251702
ÿÿÿvar(e.vil)|ÿÿÿ.2556065ÿÿÿ.0044785ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2469778ÿÿÿÿ.2645366
ÿÿÿvar(e.ban)|ÿÿÿ.2579581ÿÿÿ.0040561ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2501295ÿÿÿÿ.2660317
ÿÿÿvar(e.pis)|ÿÿÿ.2751324ÿÿÿ.0041577ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.267103ÿÿÿÿ.2834032
ÿÿÿvar(e.tec)|ÿÿÿÿ.257198ÿÿÿ.0040116ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2494545ÿÿÿÿÿ.265182
ÿÿÿvar(e.hac)|ÿÿÿ.2599377ÿÿÿ.0040369ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2521447ÿÿÿÿ.2679715
ÿÿÿvar(e.Inc)|ÿÿÿ3.46e-06ÿÿÿ.0210959ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.ÿÿÿÿÿÿÿÿÿÿÿ.
ÿÿÿvar(e.Zon)|ÿÿÿ.6527724ÿÿÿ.0183323ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6178127ÿÿÿÿ.6897104
ÿÿÿvar(e.Inf)|ÿÿÿ.6386708ÿÿÿÿ.018543ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6033419ÿÿÿÿ.6760684
ÿÿÿÿÿvar(Pob)|ÿÿÿ.7256903ÿÿÿ.0137771ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6991838ÿÿÿÿ.7532017
------------------------------------------------------------------------------
LRÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(32)ÿ=ÿ6981.06ÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000
Warning:ÿConvergenceÿnotÿachieved.

.ÿ
.ÿ//ÿDemonstratesÿthatÿtheÿequivalentÿmodelÿwithÿcovariancesÿdoesÿconverge
.ÿsemÿ///
>ÿÿÿÿÿÿÿÿÿ(cobÿitiÿayuÿ<-ÿInc)ÿ///
>ÿÿÿÿÿÿÿÿÿ(basÿzonÿvilÿ<-ÿZon)ÿ///
>ÿÿÿÿÿÿÿÿÿ(banÿpisÿtecÿhacÿ<-ÿInf),ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcovariance(Inc*ZonÿInc*InfÿZon*Inf)ÿnocnsreportÿnodescribeÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ15,254
Estimationÿmethod:ÿml

Logÿlikelihoodÿ=ÿ-157623.76

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿcobÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿitiÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.9968999ÿÿÿ.0070527ÿÿÿ141.35ÿÿÿ0.000ÿÿÿÿÿ.9830768ÿÿÿÿ1.010723
ÿÿ-----------+----------------------------------------------------------------
ÿÿayuÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.9873895ÿÿÿ.0070858ÿÿÿ139.35ÿÿÿ0.000ÿÿÿÿÿ.9735015ÿÿÿÿ1.001277
ÿÿ-----------+----------------------------------------------------------------
ÿÿbasÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿzonÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ1.001939ÿÿÿ.0073116ÿÿÿ137.04ÿÿÿ0.000ÿÿÿÿÿ.9876091ÿÿÿÿÿ1.01627
ÿÿ-----------+----------------------------------------------------------------
ÿÿvilÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ.9933183ÿÿÿ.0073277ÿÿÿ135.56ÿÿÿ0.000ÿÿÿÿÿ.9789563ÿÿÿÿÿ1.00768
ÿÿ-----------+----------------------------------------------------------------
ÿÿbanÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿpisÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿÿ.988855ÿÿÿ.0073133ÿÿÿ135.21ÿÿÿ0.000ÿÿÿÿÿ.9745212ÿÿÿÿ1.003189
ÿÿ-----------+----------------------------------------------------------------
ÿÿtecÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ1.000775ÿÿÿ.0072651ÿÿÿ137.75ÿÿÿ0.000ÿÿÿÿÿ.9865355ÿÿÿÿ1.015014
ÿÿ-----------+----------------------------------------------------------------
ÿÿhacÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ.9988858ÿÿÿ.0072792ÿÿÿ137.22ÿÿÿ0.000ÿÿÿÿÿ.9846188ÿÿÿÿ1.013153
-------------+----------------------------------------------------------------
ÿÿÿvar(e.cob)|ÿÿÿ.2318613ÿÿÿ.0039967ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2241588ÿÿÿÿ.2398285
ÿÿÿvar(e.iti)|ÿÿÿ.2366161ÿÿÿ.0040363ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2288358ÿÿÿÿ.2446609
ÿÿÿvar(e.ayu)|ÿÿÿ.2511107ÿÿÿÿ.004127ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2431508ÿÿÿÿ.2593313
ÿÿÿvar(e.bas)|ÿÿÿ.2459938ÿÿÿ.0041636ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2379672ÿÿÿÿ.2542911
ÿÿÿvar(e.zon)|ÿÿÿ.2430665ÿÿÿ.0041542ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2350592ÿÿÿÿ.2513465
ÿÿÿvar(e.vil)|ÿÿÿ.2560353ÿÿÿ.0042296ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2478783ÿÿÿÿ.2644608
ÿÿÿvar(e.ban)|ÿÿÿ.2587171ÿÿÿ.0039103ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2511655ÿÿÿÿ.2664957
ÿÿÿvar(e.pis)|ÿÿÿ.2751468ÿÿÿ.0040522ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2673182ÿÿÿÿ.2832048
ÿÿÿvar(e.tec)|ÿÿÿÿ.257568ÿÿÿ.0039009ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2500347ÿÿÿÿ.2653282
ÿÿÿvar(e.hac)|ÿÿÿÿ.260368ÿÿÿ.0039233ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.252791ÿÿÿÿ.2681721
ÿÿÿÿÿvar(Inc)|ÿÿÿ.7680732ÿÿÿ.0115314ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.7458014ÿÿÿÿÿÿ.79101
ÿÿÿÿÿvar(Zon)|ÿÿÿ.7539406ÿÿÿ.0115136ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.7317088ÿÿÿÿÿ.776848
ÿÿÿÿÿvar(Inf)|ÿÿÿ.7412173ÿÿÿ.0113505ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.7193013ÿÿÿÿ.7638011
-------------+----------------------------------------------------------------
ÿcov(Inc,Zon)|ÿÿÿ.5069948ÿÿÿ.0084842ÿÿÿÿ59.76ÿÿÿ0.000ÿÿÿÿÿÿ.490366ÿÿÿÿ.5236236
ÿcov(Inc,Inf)|ÿÿÿ.5033596ÿÿÿÿ.008397ÿÿÿÿ59.95ÿÿÿ0.000ÿÿÿÿÿ.4869018ÿÿÿÿ.5198173
ÿcov(Zon,Inf)|ÿÿÿ.5012012ÿÿÿ.0083672ÿÿÿÿ59.90ÿÿÿ0.000ÿÿÿÿÿ.4848018ÿÿÿÿ.5176006
------------------------------------------------------------------------------
LRÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(32)ÿ=ÿ141.75ÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

.ÿ
.ÿ//ÿSettingÿupÿtheÿnecessaryÿconstraintsÿtoÿgetÿconvergence
.ÿtempnameÿIncÿZonÿInf

.ÿscalarÿdefineÿ`Inc'ÿ=ÿ_b[/:var(Inc)]

.ÿscalarÿdefineÿ`Zon'ÿ=ÿ_b[/:var(Zon)]

.ÿscalarÿdefineÿ`Inf'ÿ=ÿ_b[/:var(Inf)]

.ÿconstraintÿdefineÿ1ÿ_b[/:var(e.Inc)]ÿ=ÿ`Inc'

.ÿconstraintÿdefineÿ2ÿ_b[/:var(e.Zon)]ÿ=ÿ`Zon'

.ÿconstraintÿdefineÿ3ÿ_b[/:var(e.Inf)]ÿ=ÿ`Inf'

.ÿ
.ÿ//ÿWithÿconstraints,ÿtheÿsecond-orderÿCFAÿwillÿconvergeÿ(noteÿidenticalÿlogÿlikelihoodÿetc.)
.ÿsemÿ///
>ÿÿÿÿÿÿÿÿÿ(cobÿitiÿayuÿ<-ÿInc)ÿ///
>ÿÿÿÿÿÿÿÿÿ(basÿzonÿvilÿ<-ÿZon)ÿ///
>ÿÿÿÿÿÿÿÿÿ(banÿpisÿtecÿhacÿ<-ÿInf)ÿ///
>ÿÿÿÿÿÿÿÿÿ(IncÿZonÿInfÿ<-ÿPob),ÿconstraints(1/3)ÿnocnsreportÿnodescribe

Fittingÿtargetÿmodel:
Iterationÿ0:ÿÿÿlogÿlikelihoodÿ=ÿ-167604.31ÿÿ(notÿconcave)
Iterationÿ1:ÿÿÿlogÿlikelihoodÿ=ÿ-165995.74ÿÿ(notÿconcave)
Iterationÿ2:ÿÿÿlogÿlikelihoodÿ=ÿ-163015.49ÿÿ
Iterationÿ3:ÿÿÿlogÿlikelihoodÿ=ÿ-161541.19ÿÿ
Iterationÿ4:ÿÿÿlogÿlikelihoodÿ=ÿ-158195.27ÿÿ(notÿconcave)
Iterationÿ5:ÿÿÿlogÿlikelihoodÿ=ÿ-158078.93ÿÿ(notÿconcave)
Iterationÿ6:ÿÿÿlogÿlikelihoodÿ=ÿ-157990.51ÿÿ(notÿconcave)
Iterationÿ7:ÿÿÿlogÿlikelihoodÿ=ÿ-157928.12ÿÿ
Iterationÿ8:ÿÿÿlogÿlikelihoodÿ=ÿ-157871.39ÿÿ
Iterationÿ9:ÿÿÿlogÿlikelihoodÿ=ÿÿ-157763.9ÿÿ
Iterationÿ10:ÿÿlogÿlikelihoodÿ=ÿ-157634.37ÿÿ
Iterationÿ11:ÿÿlogÿlikelihoodÿ=ÿ-157625.05ÿÿ
Iterationÿ12:ÿÿlogÿlikelihoodÿ=ÿ-157623.77ÿÿ
Iterationÿ13:ÿÿlogÿlikelihoodÿ=ÿ-157623.76ÿÿ

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ15,254
Estimationÿmethod:ÿml

Logÿlikelihoodÿ=ÿ-157623.76

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
Structuralÿÿÿ|
ÿÿIncÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿPobÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿ-----------+----------------------------------------------------------------
ÿÿZonÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿPobÿ|ÿÿÿ1.005677ÿÿÿ.0264269ÿÿÿÿ38.05ÿÿÿ0.000ÿÿÿÿÿ.9538809ÿÿÿÿ1.057473
ÿÿ-----------+----------------------------------------------------------------
ÿÿInfÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿPobÿ|ÿÿÿ1.001138ÿÿÿ.0264607ÿÿÿÿ37.83ÿÿÿ0.000ÿÿÿÿÿ.9492755ÿÿÿÿÿÿÿ1.053
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿcobÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.5805777ÿÿÿ.0072324ÿÿÿÿ80.27ÿÿÿ0.000ÿÿÿÿÿ.5664024ÿÿÿÿÿ.594753
ÿÿ-----------+----------------------------------------------------------------
ÿÿitiÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.5787779ÿÿÿ.0071932ÿÿÿÿ80.46ÿÿÿ0.000ÿÿÿÿÿ.5646794ÿÿÿÿ.5928764
ÿÿ-----------+----------------------------------------------------------------
ÿÿayuÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿIncÿ|ÿÿÿ.5732563ÿÿÿ.0071614ÿÿÿÿ80.05ÿÿÿ0.000ÿÿÿÿÿ.5592203ÿÿÿÿ.5872923
ÿÿ-----------+----------------------------------------------------------------
ÿÿbasÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ.5748249ÿÿÿ.0073459ÿÿÿÿ78.25ÿÿÿ0.000ÿÿÿÿÿ.5604271ÿÿÿÿ.5892226
ÿÿ-----------+----------------------------------------------------------------
ÿÿzonÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ.5759397ÿÿÿ.0073335ÿÿÿÿ78.54ÿÿÿ0.000ÿÿÿÿÿ.5615662ÿÿÿÿ.5903132
ÿÿ-----------+----------------------------------------------------------------
ÿÿvilÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿZonÿ|ÿÿÿ.5709841ÿÿÿ.0073119ÿÿÿÿ78.09ÿÿÿ0.000ÿÿÿÿÿ.5566531ÿÿÿÿ.5853151
ÿÿ-----------+----------------------------------------------------------------
ÿÿbanÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ.5732906ÿÿÿ.0072495ÿÿÿÿ79.08ÿÿÿ0.000ÿÿÿÿÿ.5590817ÿÿÿÿ.5874994
ÿÿ-----------+----------------------------------------------------------------
ÿÿpisÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ.5669012ÿÿÿÿ.007212ÿÿÿÿ78.61ÿÿÿ0.000ÿÿÿÿÿ.5527659ÿÿÿÿ.5810365
ÿÿ-----------+----------------------------------------------------------------
ÿÿtecÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ.5737348ÿÿÿ.0072467ÿÿÿÿ79.17ÿÿÿ0.000ÿÿÿÿÿ.5595316ÿÿÿÿÿ.587938
ÿÿ-----------+----------------------------------------------------------------
ÿÿhacÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿInfÿ|ÿÿÿ.5726518ÿÿÿ.0072494ÿÿÿÿ78.99ÿÿÿ0.000ÿÿÿÿÿ.5584432ÿÿÿÿ.5868603
-------------+----------------------------------------------------------------
ÿÿÿvar(e.cob)|ÿÿÿ.2318613ÿÿÿ.0039967ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2241588ÿÿÿÿ.2398285
ÿÿÿvar(e.iti)|ÿÿÿ.2366161ÿÿÿ.0040363ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2288358ÿÿÿÿ.2446609
ÿÿÿvar(e.ayu)|ÿÿÿ.2511108ÿÿÿÿ.004127ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2431508ÿÿÿÿ.2593313
ÿÿÿvar(e.bas)|ÿÿÿ.2459938ÿÿÿ.0041636ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2379672ÿÿÿÿ.2542911
ÿÿÿvar(e.zon)|ÿÿÿ.2430665ÿÿÿ.0041542ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2350592ÿÿÿÿ.2513465
ÿÿÿvar(e.vil)|ÿÿÿ.2560353ÿÿÿ.0042296ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2478783ÿÿÿÿ.2644608
ÿÿÿvar(e.ban)|ÿÿÿ.2587171ÿÿÿ.0039103ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2511655ÿÿÿÿ.2664957
ÿÿÿvar(e.pis)|ÿÿÿ.2751468ÿÿÿ.0040522ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2673182ÿÿÿÿ.2832048
ÿÿÿvar(e.tec)|ÿÿÿÿ.257568ÿÿÿ.0039009ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2500347ÿÿÿÿ.2653282
ÿÿÿvar(e.hac)|ÿÿÿÿ.260368ÿÿÿ.0039233ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.252791ÿÿÿÿ.2681721
ÿÿÿvar(e.Inc)|ÿÿÿ.7680732ÿÿ(constrained)
ÿÿÿvar(e.Zon)|ÿÿÿ.7539406ÿÿ(constrained)
ÿÿÿvar(e.Inf)|ÿÿÿ.7412173ÿÿ(constrained)
ÿÿÿÿÿvar(Pob)|ÿÿÿ1.510599ÿÿÿ.0537776ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.40879ÿÿÿÿ1.619765
------------------------------------------------------------------------------
LRÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(32)ÿ=ÿ141.75ÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

.ÿ
.ÿexit

endÿofÿdo-file


.

[Andrea Toledo]

Thank you so much. I did something like you. I restringed all var (e.) of the manifest variables because I had missing standard errors and I read that this parametres were unidentified. After that, I get a converges model.
I have one more question. If I keep such a restricted model, is it valid for other databases? Or do I need to change the values of the restrictions?

[Joseph Coveney]

I'm glad to hear that it worked for you.

To answer your new question: You need to fit a new model to each different set of data. So, for this, you will need to change the values to those of the new model.

[Andrea Toledo]

Thank you !!!!!!