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Re: st: SEM


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: SEM
Date   Thu, 11 Oct 2012 20:36:51 -0400

On Thu, Oct 11, 2012 at 8:14 PM, Tucker, Graeme (Health)
<Graeme.Tucker@health.sa.gov.au> wrote:
> This is a repeat post (original on 3rd October) with some code in the hope I can elicit a response from someone.
>
> I find I can fit a full orthogonal EFA in Stata using the "sem" command and get very sensible results. The problem is that the model is unidentified in other popular SEM programs (LISREL, AMOS). How does Stata get around the identification problem?
>

<snippety doo dah>

It's unidentified.

My SEM professor, the late R. P. McDonald (yes that one), gave us a
really useful rule: Standard errors in an identified model should be
proportional to 1/sqrt(n). When they are not, even if the
log-likelihood appears OK, it's not. If you convert to a standardized
solution it's MUCH easier to see this, so even if you intend to use
the unstandardized solution its worth generating the standardized
solution for inspection.

Here's the standardized output for your model (all I changed was
adding "stand" as an option), in which it is brutally apparent that
things are bad. I suspect it's just a quirk of fate (or, more likely,
simulated data) that the log-likelihood was concave and so you didn't
get a bunch of error messages.



. use http://www.stata-press.com/data/r12/sem_2fmm
. sem (L1 -> a1 a2 a3 a4 a5 c1 c2 c3 c4 c5) (L2 -> a1 a2 a3 a4 a5 c1
c2 c3 c4 c5) , covstruct(_lexogenous, diagonal) latent(L1 L2) stand

Endogenous variables

Measurement:  a1 a2 a3 a4 a5 c1 c2 c3 c4 c5

Exogenous variables

Latent:       L1 L2

Fitting target model:

Iteration 0:   log likelihood = -10309.339  (not concave)
Iteration 1:   log likelihood = -10285.537  (not concave)
Iteration 2:   log likelihood =  -10231.81  (not concave)
Iteration 3:   log likelihood = -10060.861  (not concave)
Iteration 4:   log likelihood = -9920.2176  (not concave)
Iteration 5:   log likelihood = -9726.1648  (not concave)
Iteration 6:   log likelihood = -9588.4151  (not concave)
Iteration 7:   log likelihood = -9553.7786  (not concave)
Iteration 8:   log likelihood = -9540.1666
Iteration 9:   log likelihood = -9539.3031
Iteration 10:  log likelihood =  -9534.884
Iteration 11:  log likelihood = -9534.7931
Iteration 12:  log likelihood =  -9534.793

Structural equation model                       Number of obs      =       216
Estimation method  = ml
Log likelihood     =  -9534.793

 ( 1)  [a1]L1 = 1
 ( 2)  [a2]L2 = 1
 ( 3)  [cov(L1,L2)]_cons = 0
------------------------------------------------------------------------------
             |                 OIM
Standardized |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Measurement  |
  a1 <-      |
          L1 |   .5115907   15.24519     0.03   0.973    -29.36844    30.39162
          L2 |   .7461977   10.45207     0.07   0.943    -19.73948    21.23187
  -----------+----------------------------------------------------------------
  a2 <-      |
          L1 |   .4947181   15.47373     0.03   0.974    -29.83324    30.82268
          L2 |   .7573831   10.10735     0.07   0.940    -19.05266    20.56743
  -----------+----------------------------------------------------------------
  a3 <-      |
          L1 |   .5168972   16.02201     0.03   0.974    -30.88566    31.91945
          L2 |   .7842178    10.5605     0.07   0.941    -19.91397    21.48241
  -----------+----------------------------------------------------------------
  a4 <-      |
          L1 |   .4698141   14.97014     0.03   0.975    -28.87112    29.81075
          L2 |   .7327321   9.598579     0.08   0.939    -18.08014     19.5456
  -----------+----------------------------------------------------------------
  a5 <-      |
          L1 |   .4656534   16.90655     0.03   0.978    -32.67058    33.60188
          L2 |   .8275131   9.513554     0.09   0.931    -17.81871    19.47374
  -----------+----------------------------------------------------------------
  c1 <-      |
          L1 |  -.0649107   17.44735    -0.00   0.997    -34.26109    34.13127
          L2 |   .8539805   1.326338     0.64   0.520    -1.745595    3.453556
  -----------+----------------------------------------------------------------
  c2 <-      |
          L1 |  -.0322915   17.82959    -0.00   0.999    -34.97764    34.91306
          L2 |   .8726903   .6600055     1.32   0.186    -.4208968    2.166277
  -----------+----------------------------------------------------------------
  c3 <-      |
          L1 |  -.0827462   17.59861    -0.00   0.996    -34.57539     34.4099
          L2 |   .8613845   1.690683     0.51   0.610    -2.452292    4.175061
  -----------+----------------------------------------------------------------
  c4 <-      |
          L1 |  -.1043651    17.5395    -0.01   0.995    -34.48116    34.27243
          L2 |   .8584912   2.132346     0.40   0.687    -3.320831    5.037813
  -----------+----------------------------------------------------------------
  c5 <-      |
          L1 |  -.0156541   18.14773    -0.00   0.999    -35.58455    35.55324
          L2 |   .8882625   .3202817     2.77   0.006     .2605219    1.516003
-------------+----------------------------------------------------------------
Variance     |
        e.a1 |   .1814639   .0257661                      .1373814    .2396915
        e.a2 |   .1816248   .0256626                      .1376909     .239577
        e.a3 |   .1178198   .0192061                      .0855976    .1621715
        e.a4 |   .2423784   .0318532                      .1873397     .313587
        e.a5 |    .098389   .0161366                      .0713415    .1356909
        e.c1 |   .2665038   .0365583                       .203675    .3487138
        e.c2 |   .2373689   .0328135                      .1810319    .3112381
        e.c3 |   .2511698   .0358107                      .1899358    .3321453
        e.c4 |   .2521008   .0363222                      .1900793    .3343596
        e.c5 |   .2107447   .0303307                      .1589462    .2794235
          L1 |          1          .                             .           .
          L2 |          1          .                             .           .
-------------+----------------------------------------------------------------
Covariance   |
  L1         |
          L2 |          0  (constrained)
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(25)  =     79.69, Prob > chi2 = 0.0000



-- 
JVVerkuilen, PhD
jvverkuilen@gmail.com

"Out beyond ideas of wrong-doing and right-doing there is a field.
I'll meet you there. When the soul lies down in that grass the world
is too full to talk about." ---Rumi
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