

Identification of twoindicator LC model 

Message/Author 


On page 5 of the following article, http://spitswww.uvt.nl/~vermunt/ermss2004a.pdf Vermunt & Magidson suggest that "the restrictions P(Y` = 1X = 1) = P(Y` = 2X = 2) can be used to identify a twoclass 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: Model c1: %c1#1% [u1$1] (lg1); Model c2: %c1#1% [u1$1] (lg2); MODEL CONSTRAINT: lg2 = 15  lg1; This seems far from foolproof. Is there a better way? 


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)). Also, (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) i.e. F(tau2) = 1  F(tau1) So since the logit z is obtained as z = log(F(z)/(1F(z)), you say labtau2 =  log((1F(labtau1))/F(tau1);  I think. 

Back to top 

