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 Anonymous posted on Wednesday, December 20, 2000 - 7:25 pm
In Muthen's paper(1983,1984,1995),they have a detail about WLS for categorical data.The probit model is given X(limit information) so it only apply to MIMIC model. Why they can use in general structural equation model for categorical data?
 bmuthen posted on Thursday, December 21, 2000 - 5:07 am
I think the 1995 paper gives the example of a probit Mimic, but the other two papers deal with both kinds of situations (Case A and Case B), i.e. with x variables and without x variables, so general SEM is covered in LISCOMP and Mplus.
 Anonymous posted on Thursday, December 21, 2000 - 8:37 pm
Thank you for you.In MIMIC ,we can know the distribution (y given x)is multinormal,but in M's paper(1983,1984) for case A(full information) we do not know the distribution of p(y) and p(x). How do we get it? In M's paper(1983),does full information must use E-M method ?
 Anonymous posted on Thursday, December 21, 2000 - 8:41 pm
In M's paper(1983,1984,1995) we can not get it. Can anyone provide an interpretation of the Case A(full information) produced from the detail about WLS for categorical data ?
 bmuthen posted on Friday, December 22, 2000 - 5:38 am
When xs are present, we assume y* given x normal. The marginal x distribution is not needed because we do not model it (just like regression analysis). The same actually holds if the ys are continuous. When no xs are present, we assume y* normal. Full information estimation (ML) is not used in Mplus for categorical outcomes given computational complexity, but instead limited-information (bivariate response) WLS.
 Anonymous posted on Monday, December 25, 2000 - 7:57 pm
Thank you for you.I know it apply to MIMIC model.
In M's paper(1983) how could I to count the λx in general SEM
 Anonymous posted on Tuesday, January 02, 2001 - 9:16 pm
I have some question in WLS. Does the following is yes or no ? If it is not right how can I to modify? In case A I have 3 Exogenous(x,q=3)and 4 endogenous(y,p=4).X and Y are categorial data.In general SEM model not MIMIC model,first stage I have to find the univariate probit regression(Lxi i=1-3 ; Lyj j=1-4) and use ML to find the maximun value(m1 ,m2).
Second stage use the bivariate probit regression (Li+1,i and Lj+1,j and Lij i=1-q j=1-p), i.e. to find the V(x*)'s lower triangle and V(y*)'s lower triangle and cov(x*,y*)'s lower triangle and use ML to find the value(m3) .
In final stage use the WLS to find the parameter.
 bmuthen posted on Wednesday, January 03, 2001 - 9:10 am
Yes, that is correct.
 Subert Wu posted on Friday, February 16, 2001 - 3:16 pm
Reboussin & Liang (1998) argued that three-stage GLS approach can "exprience problems of instability, bias, non-convergence, ...". What's your opinions about that?
 Bengt O. Muthen posted on Friday, February 16, 2001 - 3:55 pm
Three things. First, I think that was overstated. Second, that statement referred to the full weight matrix approach of LISCOMP (called WLS in Mplus), not the recommended, new approach in Mplus (WLSMV). WLSMV uses a diagonal weight matrix in the parameter estimation which performs much better both numerically and statistically than the old WLS. Third, the paper by Muthen-DuToit-Spisic (see the web Reference section) compares the Reboussin-Liang approach with the new Mplus approach and finds that the Mplus approach mostly performs at least as well statistically and executes much faster.
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