Average Latent Class Probabilities
Message/Author
 Scott C. Roesch posted on Saturday, August 20, 2005 - 8:11 am
I was wondering how MPlus calculates the values that appear in the "Average Latent Class Probabilities for Most Likely Latent Class Membership by Latent Class" section from an LCA. Also, are the mathematics that MPlus uses similar for a LPA.
 Linda K. Muthen posted on Saturday, August 20, 2005 - 9:20 am
For the subset of observations with the most likely class of 1, for example, the posterior probabilities for each class are averaged.
 chinthaka kuruwita posted on Friday, September 07, 2007 - 11:41 am
Hi Dr.Muthen,

I'm using M-plus ver 4.21 for my LCA. I have a 3 class model. The output gives me 3 types of class membership proportions/counts.

1. Based on the Model.
2. Based on Posterior Probabilities.
3. Based on most likely class membership.

1 and 2 are identical. Why ?

3 is different from 1 and 2. Why ?

I thought that classification into most likely class is done based on the posterior probabilities, in which case 2 and 3 should agree .

Thanks,

Chinthaka.
 Linda K. Muthen posted on Tuesday, September 18, 2007 - 5:07 am
1 and 2 are identical when the model has no restriction on the categorical latent variable distribution.

Number 3 is different because it is based on the single most likely class membership not the set of estimated posterior probabliiles for each class. They would only agree in the cae of perfect classification.
 chinthaka kuruwita posted on Friday, September 21, 2007 - 12:18 pm
Hi Dr.Muthen,

Thanks for the explanation on the posterior probabilities.

For the purpose of reporting, what counts/proportions should I use ? In my case, the model proprtions are quite similar to the classification proportions. So I guess either one is OK. But in case they differ my sizable amounts which one should we use ?

Also I get a warning message

*** WARNING in Model command
All variables are uncorrelated with all other variables within class.
Check that this is what is intended.

Thanks,

Chinthaka.
 Linda K. Muthen posted on Friday, September 21, 2007 - 3:44 pm
I would use those based on the estimated model.

The warning is just that. It can be ignored if that is what is expected.
 chinthaka kuruwita posted on Wednesday, September 26, 2007 - 10:59 am
Hi Dr.Muthen,

I'm working on a LTA model and I read the example in a paper poster on your web site and it had the following code to constrain the transition probabilities:

CLASSES : c1(3) c2(3) c3(3);
MODEL :
%OVERALL%
[c2#1](101);
[c2#2](102);
[c3#1](101);
[c3#2](102);

Could you help me in understanding what the numbers in (101) (102) mean ?

Thanks,

Chinthaka.
 Linda K. Muthen posted on Wednesday, September 26, 2007 - 11:15 am
See the transition table at the end of Chapter 13 under the heading Logistic Regression Parameterization. This shows the relationship between the transition table and the parameters in the model.
 chinthaka kuruwita posted on Wednesday, September 26, 2007 - 12:50 pm
Thanks. I have a another question. What is the difference in multinomial parametrization and the loglinear parametrization . Thank you for your help.

Chinthaka.
 Linda K. Muthen posted on Wednesday, September 26, 2007 - 1:40 pm
The logistic parameterization estimates a multinomial logistic regression. The loglinear parameterization estimates a loglinear model.
 chinthaka kuruwita posted on Thursday, September 27, 2007 - 9:54 am
Hi Dr.Muthen,

When I run my LTA model with full measurement invariant models with 3 time points I get the following warning:

There are more equality labels given than there are parameters.
Some equality labels will not be used.
Equality: 1-6

Here is my code :
%c1#1%
[vic1\$1 vic2\$1 vic3\$1 vic4\$1 vic5\$1 dep](1-6);

I want these 6 items to be the same in all 3 time points in my LTA model. What could be the reason I get this warning ?

My other question is : the class counts and proportions (for a 3 class model) I get from my LTA model are different from what I observed on the cross-sectional analysis where I did 3 LCA's for the 3 time points . What could be the reason for this?

Thanks,

Chinthaka
 Linda K. Muthen posted on Thursday, September 27, 2007 - 2:18 pm

The reason you don't get the same classes from the LTA versus the separate LCA's could be due to different observations being analyzed due to listwise deletion, equalities in the LTA which cause the model not to fit, or the need for not only first-order but perhaps second-order effects.
 chinthaka kuruwita posted on Monday, October 01, 2007 - 10:26 am
Hi Dr. Muthen,

Can we use continuous variablese (items) in LCA to determine the groups. For example, I have a depression indicator which is continuous and I used it in my corss sectional LCA to deternmine the latent classes together with another 5 binary indicators. M-plus did not give any error and I just want to find out whether we can use a continuous item in LCA ? If possible can you give me a reference to look into.

Thanks,

Chinthaka.
 Linda K. Muthen posted on Monday, October 01, 2007 - 10:34 am
Yes. Latent class indicators can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. I don't know of a reference that says this. But a model with all continuous latent class indicators is often referred to as Latent Profile Analysis.
 chinthaka kuruwita posted on Monday, October 01, 2007 - 10:48 am
Thanks.

Chinthaka.
 chinthaka kuruwita posted on Tuesday, October 09, 2007 - 10:19 am
Hi Dr.Muthen,

I have a logitudinal data set with 3 time points and at each of the time points I'm measuring a latent construct that has 3 classes using a 6 item measurement model, 5 of which are binary and one continuous item.

My LTA model gives me 35 parameters, and I do not understand how to determine the number of parameters in my model.

I used full measurement invariance and a 1st oder model with NON homogeneous transition probabilities.

Chinthaka.
 Linda K. Muthen posted on Tuesday, October 09, 2007 - 10:28 am
I don't understand your question. Are you asking about how many parameters are in a model you have estimated or how many parameters will be in a hypothetical model that you have not yet estimated.
 chinthaka kuruwita posted on Tuesday, October 09, 2007 - 12:32 pm
What I meant to ask was how Mplus calculate the number of parameters for my fitted model.

My guess was : 6 parameters for each time point for the measurement model gives 30 and I wonder what the other 5 parameters are ?

I hope this makes sense, sorry about the confusion.

Thanks,
 Linda K. Muthen posted on Tuesday, October 09, 2007 - 1:05 pm
Ask for TECH1 in the OUTPUT command to see the free parameters in the model. Also, see the Results. You will have an estimate for each of the 35 free parameters.
 Karl Hallmackenreuther posted on Tuesday, June 03, 2008 - 5:07 am
Me and my colleagues were asking us, if the following classification matrix (average Latent Class Probabilities for most likely Latent Class Membership) implies enough classfication quality to publish our 4-groups solution. We want to predict class membership.

0.807 0.026 0.090 0.076
0.018 0.797 0.115 0.070
0.028 0.044 0.890 0.039
0.031 0.103 0.094 0.771

entropy: .73

I know it isn't easy to judge, if one doesn't know all the facts but a short appraisal based on the values above would be fine! Is it very bad or something one can work on further?
Thanks!
 Linda K. Muthen posted on Tuesday, June 03, 2008 - 10:31 am
If you look at the information you provide, you see that it is class 2 that is contributing most to the low entropy. It has a large number of observations in class 3. It is not always the case that classes are distinct. It depends on what the classes are. Do the classes make sense? Does the fact that they are not distinct make sense? If you decide on these four classes, you can add covariates to the model by regressing the latent class variable on a set of covariates.
 Karl Hallmackenreuther posted on Thursday, June 05, 2008 - 11:30 am
thank you! further analysis revealed interesting outcomes. Covariates lead to higer entropy. But, BLRT points to a 3 group solution, BIC points to the 4 group solution. Since I've heard one should trust BLRT more, I decided for the 3 group solution. But, the problem here is: depending on the set (i have two possible sets) of my covariates the 3 group solution entails different of the smaller groups of the 4 group solution in both covariate sets. The 3 group solution seems not stable with respect to which of the smaller groups are isolated. Since, theoretically, all of the smaller groups from the 4 class solution make sense, I have a hard time to decide which 3 group solution I can trust more. Could that be a reason to switch back to the 4 groups?
 Bengt O. Muthen posted on Thursday, June 05, 2008 - 11:48 am
Yes. I think ultimately the interpretation is key.
 Jerry Cochran posted on Monday, December 20, 2010 - 6:13 am
Hi Dr. Muthen,

It seems that I am having a similar issue as posted above by chinthaka kuruwita, September 26, 2007 - 10:59 am. Specifically, I am trying to test model invariance as I build my LTA model. However, I keep getting this error for all of my classes as I run the constrained model:

*** WARNING in MODEL command
There are more equality labels given than there are parameters.
Some equality labels will not be used.

My syntax is:

CLASSES = c (3);
USEVAR = PYYOUDRK EVFOOLSH EVACCID EVINJSOM EVFIGHTS;

CATEGORICAL = PYYOUDRK EVFOOLSH EVACCID EVINJSOM EVFIGHTS;

ANALYSIS: TYPE = mixture;
STARTS = 150 25;
LRTSTARTS = 2 1 250 100;

MODEL:
%OVERALL%
%c#1%
[PYYOUDRK\$1 EVFOOLSH\$1 EVACCID\$1 EVINJSOM\$1 EVFIGHTS\$1] (1-5);
%c#2%
[PYYOUDRK\$1 EVFOOLSH\$1 EVACCID\$1 EVINJSOM\$1 EVFIGHTS\$1] (6-10);
%c#3%
[PYYOUDRK\$1 EVFOOLSH\$1 EVACCID\$1 EVINJSOM\$1 EVFIGHTS\$1] (11-15);

Do you have any ideas where I am going wrong?

 Linda K. Muthen posted on Monday, December 20, 2010 - 6:23 am
In the version of Mplus you are using, a list of variables must be used with a list of equality labels, for example,

[y1-y4] (1-4);

not

[y1 y2 y3 y4] (1-4);
 Jerry Cochran posted on Monday, December 20, 2010 - 9:01 am
Thank you for your help--it was right on. I really appreciate it.

Jerry
 Emmanuel Bizimungu posted on Monday, March 14, 2016 - 5:33 am
Dear Dr. Muthen,

I have identified a 4 LCA model which I want to use to predict class membership. However, I read literature that discourages using multinomial regression on grounds that it yields based estimates and biased standard errors. Could you kindly advise me on necessary modifications that I need to perform. Here is my LCA model

Class1 Class2 Class3 Class4
0.00 0.00 0.69 0.60
0.12 0.39 0.65 0.92
0.20 0.27 0.53 0.59
0.00 0.17 0.00 0.64
0.07 0.89 0.30 0.94
0.00 0.03 0.03 0.18
 Bengt O. Muthen posted on Monday, March 14, 2016 - 6:19 pm
I am not aware of literature discouraging the use of multinomial regression. You can do this "c ON x" regression in a 1-step or 3-step fashion. See

Asparouhov, T. & Muthén, B. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 21:3, 329-341. The posted version corrects several typos in the published version. An earlier version of this paper was posted as web note 15. Download appendices with Mplus scripts.
 Katharine Buek posted on Wednesday, March 21, 2018 - 3:22 pm
In my results tables, I want to report average class membership posterior probabilities... which of these two pieces of output should i use?

Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

1 2

1 0.893 0.107
2 0.143 0.857

Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

1 2

1 0.908 0.092
2 0.165 0.835
 Bengt O. Muthen posted on Wednesday, March 21, 2018 - 4:48 pm
I think you want estimated class probabilities based on posterior probabilities - given at the top of the results as

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
 Katharine Buek posted on Wednesday, March 21, 2018 - 5:04 pm
Thank you, but I'm not looking for the class counts, I want to give the classification probability, along with other info about the model like entropy and ICL.
 Bengt O. Muthen posted on Thursday, March 22, 2018 - 3:41 pm
Use the first set:

Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)