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Dear Linda/Bengt I would like to estimate factor mixture models for xsectional 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, Patrick 


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 classvarying loadings. Even a model with classvarying factor means and classinvariant intercepts is likely to have a better BIC, but far less good that the classvarying intercept model. So unless the intercepts are handled well, testing loading invariance gets drowned out by stronger signals in the data. 


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 crossnational 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 crossnational heterogeneity. might this work if the baseline model has classvarying intercepts? best wishes, Patrick 


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, Luis 


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! Kate 


1. Use the CPROBABILITIES option of the SAVEDATA command. 2. The BY statements are factor loadings. These can be greater than one. 3. Use MODEL TEST. 


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), 616. Thanks much for your time. 


I will send them to you. 


Hi, 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: https://drive.google.com/file/d/0B0eP5GG6qTFPaTFnLWE5N2dQb0U/ If it's already been formulated elsewhere, I would be greateful for the citation. Maksim 


(3) looks right, but I think (1) should condition on c and f. And I don't know what alpha is. 


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? 


Q1. I don't think it is identified. Q2. Yes, just change the lefthand side to show the conditioning. 


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), 616. Thank you. 


Sent. 


Hi, For conventional LCA model conditional item probabilities are computed using: P(yC=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(yC=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? 


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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