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 Gunda Musekamp posted on Friday, January 18, 2013 - 6:15 am
Is it possible to estimate a latent difference model for multiple groups with Mplus?

The problem I see is as follows: Usually, in latent difference models the intercept of the later state isnīt estimated (because it is determined by the mean of the first state and the mean of the latent difference variable). In multi-group analyses, Mplus estimates the intercepts of the later states (and I havenīt found a way how to tell the program that they shouldnīt be estimated). Do you have an idea how I could solve this problem?
 Bengt O. Muthen posted on Friday, January 18, 2013 - 2:55 pm
Yes, that should be possible.

Intercepts are fixed to zero by saying


[y@0];

in the relevant group.
 Gunda Musekamp posted on Monday, January 21, 2013 - 1:37 am
Thank you for your quick reply! But I guess, fixing the intercepts to zero isnīt the solution for this problem. Let me try to reformulate and clarify my question.

In latent difference models, the intercept of the later state isnīt estimated (perhaps because it can be calculated: [state2]-[state1]=[diff2-1] ==> [state2]=[state1]+[diff2-1]).

When I tried to estimate a model in a multi-group analysis (which could be estimated in single-group analysis without problems), Mplus said “THE MODEL MAY NOT BE IDENTIFIED”. The output told me that I should check the mean of the latent difference variable. Thatīs how I came to the idea to check the means and intercepts. In the preliminary results shown I noticed that in multi-group-analysis Mplus estimates the intercept of state2 (which is not the case in single-group analysis). Then I calculated if [state2]-[state1]=[diff2-1] and saw that this was not the case! How can this happen?
 Bengt O. Muthen posted on Monday, January 21, 2013 - 8:02 pm
If you want this equation to hold:

[state2]-[state1]=[diff2-1]

in group 2, you have to use Model Constraint to define the [state2] parameter as constrained in this way.
 Gunda Musekamp posted on Tuesday, January 22, 2013 - 4:13 am
Yes thatīs right, with this constraint the model can be estimated. But I noticed that the results seem implausible. In single-group analysis, the intercept of the latent difference variable is positive (e.g. 0,64). In multi-group analysis, it is negative in all groups (e.g.-3,36). Thatīs why I began to wonder, wether it is possible to estimate latent difference models in multi-group analyses with Mplus.
 Bengt O. Muthen posted on Tuesday, January 22, 2013 - 8:55 am
If the model is identified, I'm sure it can be estimated in Mplus. I just have not done this type of analysis to know how exactly it should be set up. Perhaps you want to contact those who originated it.
 Gunda Musekamp posted on Tuesday, January 22, 2013 - 10:54 pm
Dear Mr. Muthén,
thank you very much for your answers, thatīs great to have this support!
 mdehne posted on Thursday, April 18, 2019 - 2:25 am
Dear Mr. Muthén

I am trying to conduct a multigroup latent change analysis. Therefore, I used the Steyer et al. parameterization. My question is regarding the testing for group differences in the latent change scores. I realized the model as a correlated uniqeness model as follows:

MODEL: t1 by var34
var35 (1)
var34_t2@1
var35_t2 (1)
var34_t3@1
var35_t3 (1);
diff2_1 by var34_t2
var35_t2 (1);
diff3_1 by var34_t3
var35_t3 (1);

[var34 var34_t2 var34_t3] (2);
[var35 var35_t2 var35_t3] (3);

var34-var35 pwith var34_t2-var35_t2;
var34-var35 pwith var34_t3-var35_t3;
var34_t2-var35_t2 pwith var34_t3-
var35_t3;

model CG:
[t1@0 diff2_1@0 diff3_1@0];

model IG:
[t1 diff2_1 diff3_1];

Usually, the intercepts of the first indicators are fixed to be "0" to freely estimate the latent mean scores; these intercepts are now constrained to be equal across time. Is it correct to fix mean scores as specified above to test for group differences in the latent means/change scores?
 Bengt O. Muthen posted on Thursday, April 18, 2019 - 3:02 pm
Looks correct.
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