maybe these questions are a bit silly but i am new to sem and gsem and want to use it to test a model. For brevity I display the estimated model as is below. I want to model how performance, aspirations and social origin (income) influence school choice (a binary variable). For references see https://www.stata.com/manuals/sem.pdf
1. Aspirations is a latent construct generated from four ordinal variables with three levels each. I wonder how Stata generates this (continuous?) construct from the indicators. Is it possible to do this "manually" in Stata to evaluate the quality of this construct and how well this works? Like the reliability or something related. Or in other words, how can I demonstrate that it is possible and fine to generate this construct from the 4 variables?
2. Performance is another latent construct. What I understood from the manual is that the paths to school_choice are basically a logistic regression but why is performance constrained to 1 here? The manual explains this but not really how this affects interpretation (page 61). So the logit effect of performance is 1 and all other coefficients are relatively scaled to it? Can I say that aspirations are thus stronger / more important?
Code:
. gsem (aspirations -> idealabschluss, family(ordinal) link(logit)) (aspirations -> idealabsch
> luss_eltern, family(ordinal) link(logit)) (aspirations -> realabschluss, family(ordinal) lin
> k(logit)) (aspirations -> realabschluss_eltern, family(ordinal) link(logit)) (aspirations ->
> gym5, family(binomial) link(logit)) (logeinkommen -> aspirations, ) (logeinkommen -> gym5,
> family(binomial) link(logit)) (logeinkommen -> performance, ) (performance -> aspirations, )
> (performance -> gym5, family(binomial) link(logit)) (performance -> mathe3, ) (performance
> -> mathe4, ) (performance -> deutsch3, ) (performance -> deutsch4, ) (performance -> lehrerb
> ewertung, ) if wave ==6, difficult latent(aspirations performance ) nocapslatent
Fitting fixed-effects model:
Iteration 0: log likelihood = -38046.866
Iteration 1: log likelihood = -38045.233
Iteration 2: log likelihood = -38045.233
Refining starting values:
Grid node 0: log likelihood = -34637.233
Fitting full model:
Iteration 0: log likelihood = -34637.233 (not concave)
Iteration 1: log likelihood = -30344.857 (not concave)
Iteration 2: log likelihood = -29599.725 (not concave)
Iteration 3: log likelihood = -29224.302 (not concave)
Iteration 4: log likelihood = -29197.838 (not concave)
Iteration 5: log likelihood = -29168.182 (not concave)
Iteration 6: log likelihood = -29093.018 (not concave)
Iteration 7: log likelihood = -29073.603 (not concave)
Iteration 8: log likelihood = -29062.762 (not concave)
Iteration 9: log likelihood = -29018.634 (not concave)
Iteration 10: log likelihood = -28997.441 (not concave)
Iteration 11: log likelihood = -28972.917 (not concave)
Iteration 12: log likelihood = -28938.079 (not concave)
Iteration 13: log likelihood = -28920.101 (not concave)
Iteration 14: log likelihood = -28911.102 (not concave)
Iteration 15: log likelihood = -28905.134 (not concave)
Iteration 16: log likelihood = -28892.625 (not concave)
Iteration 17: log likelihood = -28866.879 (not concave)
Iteration 18: log likelihood = -28854.751 (not concave)
Iteration 19: log likelihood = -28846.679 (not concave)
Iteration 20: log likelihood = -28836.32 (not concave)
Iteration 21: log likelihood = -28831.094 (not concave)
Iteration 22: log likelihood = -28826.781 (not concave)
Iteration 23: log likelihood = -28820.993 (not concave)
Iteration 24: log likelihood = -28817.148 (not concave)
Iteration 25: log likelihood = -28815.084 (not concave)
Iteration 26: log likelihood = -28813.244 (not concave)
Iteration 27: log likelihood = -28813.061 (not concave)
Iteration 28: log likelihood = -28813.014
Iteration 29: log likelihood = -28813.224
Iteration 30: log likelihood = -28813.076
Iteration 31: log likelihood = -28813.071
Iteration 32: log likelihood = -28813.072
Iteration 33: log likelihood = -28813.073
Iteration 34: log likelihood = -28813.072
Iteration 35: log likelihood = -28813.073
Generalized structural equation model Number of obs = 6,401
Response : idealabschluss Number of obs = 5,351
Family : ordinal
Link : logit
Response : idealabschluss_elt~n Number of obs = 4,651
Family : ordinal
Link : logit
Response : realabschluss Number of obs = 5,128
Family : ordinal
Link : logit
Response : realabschluss_eltern Number of obs = 4,638
Family : ordinal
Link : logit
Response : gym5 Number of obs = 3,369
Family : Bernoulli
Link : logit
Response : mathe3 Number of obs = 4,246
Family : Gaussian
Link : identity
Response : mathe4 Number of obs = 4,410
Family : Gaussian
Link : identity
Response : deutsch3 Number of obs = 4,237
Family : Gaussian
Link : identity
Response : deutsch4 Number of obs = 4,407
Family : Gaussian
Link : identity
Response : lehrerbewertung Number of obs = 3,583
Family : Gaussian
Link : identity
Log likelihood = -28813.073
( 1) [idealabschluss]aspirations = 1
( 2) [gym5]performance = 1
----------------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
idealabschluss |
aspirations | 1 (constrained)
-----------------------+----------------------------------------------------------------
idealabschluss_eltern |
aspirations | 1.042155 .0725223 14.37 0.000 .9000138 1.184296
-----------------------+----------------------------------------------------------------
realabschluss |
aspirations | .9120171 .0482997 18.88 0.000 .8173515 1.006683
-----------------------+----------------------------------------------------------------
realabschluss_eltern |
aspirations | 2.750176 .4215265 6.52 0.000 1.923999 3.576353
-----------------------+----------------------------------------------------------------
gym5 |
logeinkommen | -.0495102 .1663453 -0.30 0.766 -.3755411 .2765206
aspirations | 1.10003 .1044508 10.53 0.000 .8953105 1.30475
performance | 1 (constrained)
_cons | -22.37072 1.725779 -12.96 0.000 -25.75319 -18.98826
-----------------------+----------------------------------------------------------------
mathe3 |
performance | .8408953 .1393619 6.03 0.000 .5677509 1.11404
_cons | .8236341 .1490849 5.52 0.000 .5314331 1.115835
-----------------------+----------------------------------------------------------------
mathe4 |
performance | .8815648 .1460884 6.03 0.000 .5952368 1.167893
_cons | .5626762 .1558728 3.61 0.000 .257171 .8681814
-----------------------+----------------------------------------------------------------
deutsch3 |
performance | .8874467 .1470255 6.04 0.000 .599282 1.175611
_cons | .5307909 .1544092 3.44 0.001 .2281544 .8334275
-----------------------+----------------------------------------------------------------
deutsch4 |
performance | .9502487 .1572729 6.04 0.000 .6419996 1.258498
_cons | .2418313 .1644166 1.47 0.141 -.0804194 .564082
-----------------------+----------------------------------------------------------------
lehrerbewertung |
performance | .9363136 .1552998 6.03 0.000 .6319316 1.240696
_cons | -.0363143 .1649169 -0.22 0.826 -.3595455 .2869169
-----------------------+----------------------------------------------------------------
aspirations |
performance | 2.88466 .5057989 5.70 0.000 1.893312 3.876008
logeinkommen | .8647389 .1046278 8.26 0.000 .6596721 1.069806
-----------------------+----------------------------------------------------------------
performance |
logeinkommen | .4601273 .0758535 6.07 0.000 .3114572 .6087974
-----------------------+----------------------------------------------------------------
/idealabschluss |
cut1 | 15.3001 1.13888 13.06793 17.53226
-----------------------+----------------------------------------------------------------
/idealabschluss_eltern |
cut1 | 16.21353 1.184927 13.89112 18.53595
-----------------------+----------------------------------------------------------------
/realabschluss |
cut1 | 15.09398 .9326309 13.26606 16.92191
-----------------------+----------------------------------------------------------------
/realabschluss_eltern |
cut1 | 45.71751 6.376759 33.2193 58.21573
-----------------------+----------------------------------------------------------------
var(e.aspirations)| 3.187809 .3478379 2.574029 3.947946
var(e.performance)| .4555128 .1509999 .2378659 .8723064
-----------------------+----------------------------------------------------------------
var(e.mathe3)| .2587328 .0072316 .2449404 .2733018
var(e.mathe4)| .2667887 .0074515 .2525766 .2818004
var(e.deutsch3)| .2163404 .0064982 .2039717 .229459
var(e.deutsch4)| .20087 .0064828 .1885575 .2139864
var(e.lehrerbewertung)| .2471626 .0081774 .2316438 .263721
----------------------------------------------------------------------------------------
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