Dear all,

I know that gsem allows only the logit link for the multinomial response variable, but instead of mlogit, a part of my structural equation model needs a mprobit, so I wonder if it's possible to trick gsem to fit a mprobit model.

To see if it's possible to do so, I try to use gsem to replicate the example in the mprobit help file. As can be seen from the code and output below, I fail, so I'm here to seek your advice and help. Do I mess up any model specification?

Code:
webuse sysdsn1, clear

//#The mprobit to be replicated:
mprobit insure age male nonwhite i.site, baseoutcome(3)
estimate store Mprobit
keep if e(sample)

ge insure1 =insure==1 if insure !=. & insure!=2
ge insure2 =insure==2 if insure !=. & insure!=1

//#Try to replicate mprobit using gsem below:
gsem (insure1 <- age male nonwhite i.site L1@1, probit)  ///
     (insure2 <- age male nonwhite i.site L1@1, probit), ///
     var(L1@1) means(L1@0)
estimate store GsemMprobit

estimate table Mprobit GsemMprobit, equations(1:1, 2:2) stats(N ll)

----------------------------------------
    Variable |  Mprobit     GsemMpro~t  
-------------+--------------------------
#1       age |  .00508145    .00267706  
        male |  -.3332637   -.25006264  
    nonwhite | -.24858591   -.09825171  
     site 2  |  .68994846    .82667674  
          3  |  .17884471    .08275221  
          L1 |                       1  
       _cons |  .98559174    1.5189577  
-------------+--------------------------
#2       age | -.00477215   -.00224479  
        male |  .14420407    .02492026  
    nonwhite |  .57591439    .48949647  
     site 2  |  .78734408    .90338986  
          3  | -.31704734   -.26848647  
          L1 |                       1  
       _cons |  1.2087417    1.5969324  
-------------+--------------------------
      var(L1)|                       1  
-------------+--------------------------
Statistics   |                          
           N |        615          615  
          ll | -534.52833   -204.97804  
----------------------------------------


Moreover, I also read the gsem manual (https://ift.tt/Zma5TDu), in case it's impossible to trick gsem to fit mprobit and I need to programme it by myself. I have two questions about the linear prediction:

1. as the quote below, why do the latent loadings Λi for an observed response variable yij form a matrix instead of a vector? (Note that yij is not a vector but a scalar.)

2. why is the vector of exogenous variables xj placed in the product of xj'Λiu? (u is a vector of latent variables.) I thought it should be just the product of the latent variables u and their regression coefficients (loadings Λi) for yij.

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Any comments and suggestions will be appreciated, and I hope the questions above do not violate any regulation of this forum. Thank you very much.