Conditional probabilities in LCA PreviousNext
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 Marius Gerber posted on Tuesday, March 06, 2007 - 12:29 am
I have a question concerning the conditional probabilities in LCA. Usually, you assign a person to the latent class with the highest probability and then go on with this categorial variable. However, is it not allowed to go on with the probabilities themselves, meaning that you get and calculate with a score for each person and each class? I know that one requirement of LCA is that latent classes are disjunctive and exhaustive. I calculated my analyses with both the categorial variable (= a person belongs to one and only one latent class) and the (intervall scaled) probabilities (= a person has a value for each class). The results seem to me much more plausible using the scores... And in my case it's reasonnable to assume that a person "has" a bit of different classes.

Thank you so much for your help!
 Linda K. Muthen posted on Tuesday, March 06, 2007 - 8:19 am
Given that the LCA is estimated with individuals in all classes, using most likely class membership would introduce estimation errors. In Mplus one can add covariates or other relationships to the model and estimate it in one step.
 Jon Heron posted on Wednesday, March 07, 2007 - 3:37 am
Hi Marius,

like you, I've recently had the same thoughts that a model using the posterior probabilities themselves is the way to go (e.g. an mlogit model with pweights in Stata).

Unfortunately, any model which starts off by you importing the data into another package will end up treating your derived class variable/probabilities as manifest whereas they are actually still latent.

Two issues here

1) You're going to underestimate SE's if you assume the class-variable is manifest. I guess it's the same as imputing some missing data and then assuming your dataset is complete.

2) To fit the model properly, the other variables which you bring into your model once you've derived the latent classes should at the very least be permitted to affect the posterior probabilities and with a model including covariates these should be allowed to affect the 'curves' themselves and hence potentially the interpretation of the classes.

This second point is currently causing me serious brain-ache.

Check out:

Delucchi, Matzger, Weisner
Drug and Alcohol Dependence 74 (2004) 235244
Dependent and problem drinking over 5 years: a latent class growth analysis

For quite a clear stats-methods on the way to proceed
 Bengt O. Muthen posted on Wednesday, March 07, 2007 - 6:54 pm
Just a comment on using posterior-probability-weighted multinomial regression for exploring "c ON x" relationships. There is no need for going outside Mplus here - you can do multinomial regression and instead of categorical observed dependent variable categories such as 0, 1, 2, 3 use fractional membership in all dependent variable categories.
 Marius Gerber posted on Thursday, March 08, 2007 - 6:26 am
Thank you for your answers. I have to explain in more detail what I did. My aim is to predict work outcomes with the clustered variables. That is, I do not predict membership of classes but instead use the classification variable as IV.

I did 2 steps: first I calculated an exploratory latent class analysis and found 4 classes (with PANMARK). In the next step (with SPSS) I used these class-variable as an IV and/or as a moderator in multiple regression analysis to predict work outcomes. Here, I did not use 4 binary IV (for each class) but 4 variables with the response probabilites of the LCA solution. This means that I have a (intervall scaled) number for each person and each class. This is against the idea that a person can only belong to one class, but in my case, I find it very plausible that a person does belong to different classes. Or is latent class analysis simply the wrong method if my assumption is that a person can be member of different classes? Or is it possible to introduce the condition that a person can be member of various classes in LCA? Is my approach described above justifiable?

I'm very grateful for your answers.
 Bengt O. Muthen posted on Thursday, March 08, 2007 - 9:24 am
If you want to study

c--> y

for a latent class variable c and an observed outcome variable y, you can do this in one step in Mplus. A one-step analysis avoids errors of estimation for the parameters and their SEs. You don't say "y ON c", but the means/intercepts/thresholds will change by default across the c classes. Ex8.6 in the UG shows how to do this for a categorical outcome in the context of a growth mixture model.

If you prefer to think of a person as belonging to several classes, LCA is not the model to use. LCA assumes that a person belongs to only one class. Although the class probabilities that you get at the end gives a person a probability for each class, that is not a feature of the model. It should rather be viewed in line with factor score estimation where each person gets a posterior distribution (given the model and his/her data) and his/her estimated factor score is taken as the peak of that posterior distribution (like most likely class). If you want the model itself to acknowledge partial class membership you are into modeling such as "Grade of Membership". GoM is discussed in the Mplus framework in section 7 of Asparouhov-Muthen (2006) on our web site under Papers, Multilevel Mixture Modeling.
 Marius Gerber posted on Monday, March 12, 2007 - 10:18 am
Dear Bengt, thanks a lot for your answer.
"Grade of membership" seems to be what I need. Up to now, I used PANMARK and Mplus for LCA. Can I calculate GoM with them or which program instead is required?
 Bengt O. Muthen posted on Saturday, March 17, 2007 - 10:48 am
You can use Mplus for Grade of Membership modeling. GoM is discussed in the Mplus framework in section 7 of Asparouhov-Muthen (2006) on our web site under Papers, Multilevel Mixture Modeling.
 Marius Gerber posted on Friday, May 18, 2007 - 5:26 am
Dear Bengt,
Can you please tell me what the mplus command is to calculate a grade of membership model? I have read the Asparouhow/Muthen paper (2006) and went through the user guide, but was not able to find the command for this special type of lca.
Thanks a lot, Marius
 Bengt O. Muthen posted on Monday, May 21, 2007 - 3:35 pm
We will put together a brief Mplus Web Note to show the steps of doing GoM as discussed in the Asparouhov-Muthen paper. The note will be available probably tomorrow.
 Marius Gerber posted on Tuesday, June 19, 2007 - 4:56 am
I'm sorry for asking repeatedly. I cannot find an Mplus Web Note showing the steps of GoM. Has it not been published yet?
 Linda K. Muthen posted on Tuesday, June 19, 2007 - 7:12 am
I'm sorry that it has not been put on the website yet. It is done and has been tried out by a tester. We will try to get it up in the next few days. Send me your email address if you need it sooner.
 Nick Shryane posted on Monday, November 24, 2008 - 6:43 am
I'd also really appreciate seeing the web note on Grade of Membership models, but I can't find it on the webnotes page (
Nick Shryane
 Linda K. Muthen posted on Monday, November 24, 2008 - 7:54 am
See Section 7 of the following paper which is available on the website:

Asparouhov, T. & Muthen, B. (2008). Multilevel mixture models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 27-51. Charlotte, NC: Information Age Publishing, Inc.
 Nick Shryane posted on Monday, November 24, 2008 - 4:59 pm
Hello Linda,
Thanks for the reference. I must admit I'm struggling to convert the general GoM model specification from the paper into something concrete in the Mplus language. Is it something along the lines of example 10.7 in the user's guide? Can you also tell me how one should properly incorporate the dummy variables for items (Xqij)?
Any advice appreciated,
 James Gambrell posted on Saturday, May 08, 2010 - 1:41 pm
Why has this note still not been published?
 Linda K. Muthen posted on Monday, May 10, 2010 - 8:31 am
This is difficult to do and we had hoped to simplify it. Obviously we have not yet done this. I have a mixture input that I can send you but I can't offer much beyond that.
 IYH Boon posted on Friday, February 24, 2012 - 1:29 pm
Is there any update on this matter? I'd like to estimate GoM models using Mplus, and I would very much benefit from a snippet of example code.
 Linda K. Muthen posted on Saturday, February 25, 2012 - 7:53 am
This is still on our list but we have not gotten to it yet.
 Dan Kahan posted on Friday, June 22, 2012 - 6:23 am
I'd love to use Mplus (or any other application) to do GoM modeling.

Basically, your responses go like this:

3/17/2007: "You can use Mplus for Grade of Membership modeling."

5/21/2007: "We will put together a brief Mplus Web Note to show the steps of doing GoM as discussed in the Asparouhov-Muthen paper. The note will be available probably tomorrow."

6/19/2007: "It is done ... We will try to get it up in the next few days"

11/24/2008: "see Section 7 of the following paper" (advice that a reader reported was not helpful)

5/10/2010: "this is difficult ... not yet done";

2/25/2012: "still on our list but we have not gotten to it yet..."

Am I right to infer that Mplus really *can't* do GoM?
 Linda K. Muthen posted on Friday, June 22, 2012 - 9:27 am
Yes, Mplus does not do GoM. GoM is best done by Bayesian analysis which Mplus now has. GoM is on our Bayes list but many other important Bayes developments are higher on that list.
 Bengt O. Muthen posted on Friday, June 22, 2012 - 10:17 am
Section 7 in

shows how this can be done in Mplus with the ML estimator. It may not be easy, however, as the reader commented.
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