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st: SEM
From
"Tucker, Graeme (Health)" <[email protected]>
To
"'[email protected]'" <[email protected]>
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: [email protected]
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