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 patrick sturgis posted on Friday, February 27, 2009 - 6:37 am
Dear Linda/Bengt

I would like to estimate factor mixture models for x-sectional data in which factor loadings are free to vary across classes, so that the number of classes is determined by population heterogeneity in the factor loadings. I have two questions about this; 1. is it technically possible? 2. would this be feasible as a means of assessing measurement invariance (i.e. if optimal number of classes = 1, there is no variability in loadings)? thanks,

 Bengt O. Muthen posted on Friday, February 27, 2009 - 9:31 am
1. It is technically possible.

2. I don't think so for reasons below.

In my experience, what varies most across classes in factor mixture models are the indicator intercepts (just like in LCA/LPA). Such a model will most likely have a much better BIC than a model with only class-varying loadings. Even a model with class-varying factor means and class-invariant intercepts is likely to have a better BIC, but far less good that the class-varying intercept model. So unless the intercepts are handled well, testing loading invariance gets drowned out by stronger signals in the data.
 patrick sturgis posted on Saturday, February 28, 2009 - 2:52 am
Dear Bengt, many thanks for that. I had wondered whether the factor mixture model approach might be a way of assessing measurement invariance in a cross-national survey that could incorporate differences in sample composition across countries. the standard MGA approach assumes that if loadings/intercepts are not equal across countries, this is due to differences in the meaning of the questions. but it seems reasonable that it could also be due to differences in population characteristics (e.g. more educated people in one country than another). in a FMM context one could include these type sof variables and country dummies as covariates on the latent class variable. that is, it would be a way of testing for country differences controlling for observed sources of cross-national heterogeneity. might this work if the baseline model has class-varying intercepts? best wishes,

 Luis Garrido posted on Monday, March 09, 2009 - 9:49 am
I'm running a factor mixture analysis with 12 categorical indicators (3 response options) and 1 factor. From previous analysis with similar data I've been able to ascertain that the people in one of the latent classes hardly ever choose a certain response option. The problem I seem to have now is that some items have zero frequency (instead of a low frequency) for certain categories and I think this may be causing the estimation to have problems (such as running slower and not converging). Collapsing categories wouldn't make sense since this is an important difference between the groups that would be lost if that were done.

What can I do to get around this problem? Thanks for your help,

 Linda K. Muthen posted on Monday, March 09, 2009 - 6:56 pm
If categories were zero, the thresholds would be fixed. Please send your input, data, output, and license number to support@statmodel.com.
 Kate posted on Monday, April 25, 2011 - 5:04 pm
Hello, Linda/Bengt

I have a few questions on the Mplus output of factor mixture model.
(1)How can I see the posterior probabilities of cluster membership, as well as cluster assignment of individual (which cluster dose each individual belong to) ?
(2)Dose the value ¡° F4 BY D1¡± means the factor load? Sometimes I found that this kind of value exceeds 1, is it possible?
(3)If I would like to tested whether the parameter difference between class is statistically significant, what kind of command should I use? Or should I conduct some extra statistics?

Many thanks!

 Linda K. Muthen posted on Monday, April 25, 2011 - 5:47 pm
1. Use the CPROBABILITIES option of the SAVEDATA command.
2. The BY statements are factor loadings. These can be greater than one.
 Kathleen Rowan posted on Sunday, January 19, 2014 - 8:44 pm
Would it be possible to post the syntax used in Dr. Muthén's 2006 paper, "Should substance use disorders be considered as categorical or dimensional?" in Addiction, 101 (Suppl. 1), 6-16.

Thanks much for your time.
 Bengt O. Muthen posted on Monday, January 20, 2014 - 5:09 pm
I will send them to you.
 Maksim Rudnev posted on Thursday, May 07, 2015 - 5:49 pm

I am trying to write a formulation of factor mixture model generalized from Example 7.27. I am highly unsure if it's correct. Could you please have a look at it and say whether it is ok?

Here is a link to formulas:

If it's already been formulated elsewhere, I would be greateful for the citation.

 Bengt O. Muthen posted on Friday, May 08, 2015 - 8:30 am
(3) looks right, but I think (1) should condition on c and f. And I don't know what alpha is.
 Maksim Rudnev posted on Saturday, May 09, 2015 - 3:19 am
Thank you for the answer!

Alpha is a global intercept, like in all loglinear models. Should I remove it from (1)?

Is the right part of (1) is ok, except for alpha?
 Bengt O. Muthen posted on Sunday, May 10, 2015 - 3:25 pm
Q1. I don't think it is identified.

Q2. Yes, just change the left-hand side to show the conditioning.
 'Alim Beveridge posted on Sunday, March 27, 2016 - 12:47 am
Dear Drs. Muthén,

I would also like to ask for the syntax used in Bengt's 2006 paper, "Should substance use disorders be considered as categorical or dimensional?" in Addiction, 101 (Suppl. 1), 6-16.

Thank you.
 Bengt O. Muthen posted on Sunday, March 27, 2016 - 10:07 am
 Maksim Rudnev posted on Sunday, May 08, 2016 - 1:59 am

For conventional LCA model conditional item probabilities are computed using:
P(y|C=1) = exp(threshold1)/(1+ exp(threshold1))

However, when a factor is added in example 7.27б the above formula doesn't work.

I assumed factor loadings to be slopes, i.e.
P(y|C=1) = exp(Floading1 + threshold1) / (1 + exp(Floading1 + threshold1)),
but it did not match Plot3 estimated item probabilities.

What is the correct way for computing conditional item probabilities in factor mixture model from Example 7.27?
 Bengt O. Muthen posted on Monday, May 09, 2016 - 2:22 pm
The estimated item probabilities are not item probabilities conditioned on the factor but marginal probs (for that class). This involves numerical integration over the factor which is hard to do by hand.

You can compute item probabilities conditional on the factor (and class) by choosing certain factor values and multiply them by the factor loading as you have indicated.
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