Categorical indicators & thresholds
Message/Author
 Guillaume Filteau posted on Tuesday, October 28, 2008 - 2:24 pm
Hello,

I have three questions regarding LCA and categorical indicators.

First, thresholds seem to be interpretable as cutpoints of a latent response variable. However, what is the distribution of said latent variable? Is it assumed normal?

Also, in case of interval data, is it possible to constrain the thresholds to be at equal distance from each other?

Finally, what about cases where an “I don’t know” option (or similar) is added to a Likert item? Would it be a good idea to separate the item into one dummy variable (know/don't know) and one ordinal variable?

Best,
Guillaume
 Linda K. Muthen posted on Tuesday, October 28, 2008 - 3:07 pm
In logistic regression, it is a logistic distribution.

If by interval, you mean ordered categorical, the answer is yes.

There is a huge literature on how to handle "I don't know". I don't know if there is one preferred way.
 Guillaume Filteau posted on Tuesday, October 28, 2008 - 8:40 pm
So in ordinal LCA, the thresholds are for a logistic model. I was confused because in nominal LCA, the thresholds are logit.
As for constraining the thresholds to be equidistant, I tried doing it this way, but it does not seem to be working:

.....
%c#2%
[u1\$1*-1] (t1);
[u1\$2* 0] (t2);
[u1\$3* 1] (t3);

MODEL CONSTRAINT:
t3 = 2*t2 - t1;
.....

 Guillaume Filteau posted on Tuesday, October 28, 2008 - 8:58 pm
You can ignore my previous comment about logit. I found my answer in the Mplus 3 Technical Appendix, page 30.
 Guillaume Filteau posted on Tuesday, October 28, 2008 - 10:38 pm
I have a new question about thresholds (on top of the equidistant thresholds issue):

Mplus output reports not only all the estimated thresholds, but also K -1 "categorical latent variables means".

How can these means be interpreted, and how is it possible to estimate them on top of the thresholds and still get an identified model?

Thank you very much for your support,
Guillaume
 Linda K. Muthen posted on Wednesday, October 29, 2008 - 8:06 am
The k-1 categorical latent class means are the logits for the latent class probabilities. They can be identified in addition to the thresholds. A good reference for latent c lass analysis is:

Hagenaars, J.A. & McCutcheon, A.L. (2002). Applied latent class analysis. Cambridge, UK: Cambridge University Press.