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st: SEM


From   "Tucker, Graeme (Health)" <Graeme.Tucker@health.sa.gov.au>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: SEM
Date   Fri, 12 Oct 2012 10:44:57 +1030

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?

This was run in version 12.1 of Stata on Microsoft Windows XP Professional Version 5.1.2600 Service Pack 3 Build 2600.

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)

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
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Measurement  |
  a1 <-      |
          L1 |          1  (constrained)
          L2 |   1.011864   .6722794     1.51   0.132    -.3057798    2.329507
  -----------+----------------------------------------------------------------
  a2 <-      |
          L1 |   .9415674   1.394669     0.68   0.500    -1.791934    3.675069
          L2 |          1  (constrained)
  -----------+----------------------------------------------------------------
  a3 <-      |
          L1 |   .8112258   .9734421     0.83   0.405    -1.096686    2.719137
          L2 |   .8538175   .1119264     7.63   0.000     .6344458    1.073189
  -----------+----------------------------------------------------------------
  a4 <-      |
          L1 |   .9174787     1.8963     0.48   0.629    -2.799201    4.634158
          L2 |   .9926725   .2509752     3.96   0.000     .5007701    1.484575
  -----------+----------------------------------------------------------------
  a5 <-      |
          L1 |   .9155148   5.958346     0.15   0.878    -10.76263    12.59366
          L2 |   1.128673   2.087061     0.54   0.589     -2.96189    5.219237
  -----------+----------------------------------------------------------------
  c1 <-      |
          L1 |  -.0705726   21.07223    -0.00   0.997    -41.37139    41.23025
          L2 |   .6441078   9.596012     0.07   0.946    -18.16373    19.45195
  -----------+----------------------------------------------------------------
  c2 <-      |
          L1 |  -.0380796   22.16024    -0.00   0.999    -43.47135    43.39519
          L2 |   .7139302   10.06727     0.07   0.943    -19.01756    20.44542
  -----------+----------------------------------------------------------------
  c3 <-      |
          L1 |   -.118145   28.64796    -0.00   0.997    -56.26712    56.03083
          L2 |   .8532089   13.06077     0.07   0.948    -24.74543    26.45185
  -----------+----------------------------------------------------------------
  c4 <-      |
          L1 |  -.1321534   26.14768    -0.01   0.996    -51.38067    51.11636
          L2 |   .7541362   11.93717     0.06   0.950    -22.64228    24.15055
  -----------+----------------------------------------------------------------
  c5 <-      |
          L1 |  -.0182964   21.75617    -0.00   0.999     -42.6596    42.62301
          L2 |   .7202277   9.870919     0.07   0.942    -18.62642    20.06687
-------------+----------------------------------------------------------------
Variance     |
        e.a1 |    368.118   43.96268                      291.2942    465.2027
        e.a2 |   349.3047   41.43099                      276.8493    440.7226
        e.a3 |   154.0761   21.51316                      117.1884     202.575
        e.a4 |   490.7676   54.86998                       394.192    611.0039
        e.a5 |   201.9267   28.16974                      153.6197    265.4241
        e.c1 |   167.2573   20.13605                       132.102    211.7683
        e.c2 |   175.2571   20.91835                      138.7004    221.4488
        e.c3 |   271.8595   34.08544                      212.6287    347.5899
        e.c4 |   214.6162   27.28902                      167.2746    275.3564
        e.c5 |    152.853   18.94199                      119.8922    194.8756
          L1 |   530.9359   31643.37                      9.86e-49    2.86e+53
          L2 |   1103.216   29445.29                      2.11e-20    5.78e+25
-------------+----------------------------------------------------------------
Covariance   |
  L1         |
          L2 |          0  (constrained)
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(25)  =     79.69, Prob > chi2 = 0.0000

. 
end of do-file

. do "C:\DOCUME~1\tuckerg\LOCALS~1\Temp\STD06000000.tmp"

. estat gof,stat(all)

----------------------------------------------------------------------------
Fit statistic        |      Value   Description
---------------------+------------------------------------------------------
Likelihood ratio     |
         chi2_ms(25) |     79.695   model vs. saturated
            p > chi2 |      0.000
         chi2_bs(45) |   2467.161   baseline vs. saturated
            p > chi2 |      0.000
---------------------+------------------------------------------------------
Population error     |
               RMSEA |      0.101   Root mean squared error of approximation
 90% CI, lower bound |      0.076
         upper bound |      0.126
              pclose |      0.001   Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
                 AIC |  19129.586   Akaike's information criterion
                 BIC |  19230.844   Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison  |
                 CFI |      0.977   Comparative fit index
                 TLI |      0.959   Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals    |
                SRMR |      0.016   Standardized root mean squared residual
                  CD |      0.995   Coefficient of determination
----------------------------------------------------------------------------


Graeme Tucker
Tel: 61 8 8226 6358
Email: graeme.tucker@health.sa.gov.au 

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