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Identification of two-indicator LC model
Latent Variable Mixture Modeling
posted on Monday, May 22, 2006 - 11:59 am
On page 5 of the following article,
Vermunt & Magidson suggest that "the
restrictions P(Y` = 1|X = 1) = P(Y` = 2|X = 2) can be used to identify a
two-class model with two dichotomous indicators"
My trouble is that I don't see an easy way to implement this constraint in MPlus. One idea I had was something like this, based on the idea that the maximum logit threshold is 15:
lg2 = 15 - lg1;
This seems far from foolproof. Is there a better way?
Bengt O. Muthen
posted on Tuesday, May 23, 2006 - 1:12 am
It is a little tricky since your restriction is on the probability scale and your parameters are on the logit scale. But you can do it as follows.
Note that for a given item,
(1) P(y=2 | x=2) = F(-tau2)
where x is the latent class variable, tau2 is the Mplus threshold parameter for class 2, and F is the logistic function,
F(z) = 1/(1+exp(-z)).
(2) P(y=1 | x=1) = 1 - P(y=2 | x=1)
= 1 - F(-tau1).
You should give a label to tau1 and tau2 in the Model statements, then use those 2 labels in Model constraint to apply the required contraint
(1) = (2)
F(-tau2) = 1 - F(-tau1)
So since the logit z is obtained as
z = log(F(z)/(1-F(z)),
labtau2 = - log((1-F(-labtau1))/F(tau1);
- I think.
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