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Mplus Discussion > Categorical Data Modeling >
 Stephanie Fitzpatrick posted on Sunday, November 20, 2011 - 1:52 pm

I have a 2 class latent profile model and I want to compare these two profiles on prevalence/probability of prediabetes. Prediabetes is a binary outcome. I am not sure of the syntax to use.

I would think the syntax should be x on C, but this seems to only work when I just put Categorical Are x and nothing in the Model statement except the %Overall%. However, the output that I receive does not seem to tell me if the probabilities for one class are different for the other. See output below. Please advise. Thanks


Latent Class 1

Category 1 0.968 0.017 58.319 0.000
Category 2 0.032 0.017 1.920 0.055

Latent Class 2

Category 1 0.818 0.084 9.689 0.000
Category 2 0.182 0.084 2.158 0.031


Latent Class 1 Compared to Latent Class 2

Category > 1 0.148 0.116 1.270 0.204
 Bengt O. Muthen posted on Sunday, November 20, 2011 - 8:23 pm
It sounds like you have a set of continuous latent class (latent profile) indicators from which you form 2 classes and in that same analysis you want to compare the probability of another variable u=prediabetes, across those 2 classes. If that's a correct understanding, you don't say u on c because the u probabilities vary across the classes as the default - the output gives you different thresholds in logit scale for the 2 classes, and those logits can be translated into probabilities as

P = 1/(1+exp(threshold))

You can test the differences in Model Constraint, creating a New parameter that is the difference in thresholds, or probabilities, across the 2 classes.
 Stephanie Fitzpatrick posted on Monday, November 21, 2011 - 3:42 pm
Thanks for your reply Dr. Muthen and your understanding is correct in that I want to compare the probability of u across the 2 latent profiles. What exactly is the syntax for this? It seems you are suggesting to look at the thresholds. Does the response in probability scale not give me what I need? Also, keep in mind that u is binary. Thank you.
 Bengt O. Muthen posted on Tuesday, November 22, 2011 - 6:28 pm
If you get results in probability scale for the distal u in the two classes, those are the ones you want to compare. If you want a statistical test of their difference, you have to express the difference either in terms of logits or in terms of probabilities using Model Constraint. In doing so, you give labels to the threshold for u in each class in your Model command, and then use Model constraint to express a new parameter that is their difference - this also gives you a z test of the difference.
 Melissa Yale posted on Tuesday, May 15, 2012 - 2:16 pm
I am running a latent profile analysis with a distal outcome variable. I have a set of continuous latent class indicators from which I am forming 4 latent classes. In that same analysis I want to add a distal outcome variable and compare the probabilities across the 4 classes. The outcome variable is a 5 category nominal variable. In my output I am only getting mean values for 4 of the 5 nominal categories under each class. My questions are how do I interpret these mean values/estimates? Should different output (probabilities) be present?

Secondly, I labeled the parameters of each nominal category differently for each class and then created new parameters for use in the MODEL CONSTRAINT command. For example %c#1%
[u#1] (p1);
[u#1] (p2);
Model Constraint: New (T1);
T1 = p1 - p2;

What is the estimate and p-value given for this new parameter in the output? Also, Mplus will not let me create a parameter for all 5 categories. How do I do class to class comparisons for the 5th category?

Any guidance would be much appreciated.
 Bengt O. Muthen posted on Tuesday, May 15, 2012 - 6:45 pm
Take a look at our Topic 2 handout on our web site, slides 58 and on. That shows how to compute the probabilities based on the logits. You have only intercepts beta_0c in the slide 58 multinomial expression (no x's), and they vary over your latent classes.

I don't know if you want to constrain logits or constrain probabilities of certain nominal categories. Both can be done in Model Constraint, but the probabilities would first have to be expressed from the logits as per above.
 Melissa Yale posted on Thursday, May 17, 2012 - 11:53 am
Thank you.

Just for clarification:
If the means for Class 1 in the output are
U#1 -0.811
U#2 -0.493
U#3 -0.185
U#4 0 (reference)
AND the means for Class 2 are
U#1 -0.198
U#2 -0.043
U#3 -0.156
U#4 0 (reference)
AND the means for Class 3 are
U#1 -0.830
U#2 -0.378
U#3 -1.412
U#4 0 (reference)

I would calculate the probability of U#1 in Class 3 by p13= exp (-0.830)/(exp(-0.830)+exp(-0.378)+exp(-1.412)+1)
then do the same for U#1 in class 2 (p12) and Class 1 (p11). Then calculate the difference of probabilities between classes for u#1 as p13-p12?
 Linda K. Muthen posted on Friday, May 18, 2012 - 12:09 pm
That is correct.
 Jen Rose posted on Tuesday, January 20, 2015 - 10:14 am
I have a 3 class LCA and I'm trying to figure out what the logistic regression odds ratio is comparing for the differences between classes on the covariates. Is it the between class ratio of the differences in probabilities for the levels of the binary covariate within each class?

So, for example, I have the following model estimated probabilities for a covariate assessing whether or not a respondent has some college education

At least some college education

Class 1 Class 2 Class 3
No .52 .29 .19
Yes .58 .29 .12

and I have an odds ratio comparing Class 1 to Class 3 equal to 1.68. How is that odds ratio calculated? Is it possible to convert the odds ratio to a prevalence ratio?
 Bengt O. Muthen posted on Tuesday, January 20, 2015 - 1:59 pm
The OR for those probabilities should be

------- = 1.77

If you send the output to Support we may be able explain why this isn't 1.68.
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