Mixture model analysis wtih categoric... PreviousNext
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 Anonymous posted on Wednesday, April 20, 2005 - 11:54 pm
Hi Prof. Muthen

In regular SEM with categorical indicators, Mplus allows for DELTA and THETA parameterization.

In mixture analysis, which parameterization is using in mplus? I tried to specify THETA or DELTA when running mixture analysis, but both give me errors in Mplus output. I would like to use THETA parameterization so I can constrain the residual variance to be 1.

Please let me know.
Thanks a lot!!!
 bmuthen posted on Thursday, April 21, 2005 - 12:27 am
Delta and Theta parameterizations are only used with probit, not with the logit formulation that is used in mixture modeling. There are no residual variance parameters in the logit formulation - for logit you can think of the residual variance for the underlying continuous response variable as having a logistic density with variance fixed at pi-squared/3 (see logistic density refs). So, the res var is in this sense already fixed.
 Dena Pastor posted on Thursday, August 03, 2006 - 4:50 pm
I am trying to run a mixture factor model (not factor mixture model) with 12 dichotomous indicators. I have a single factor underlying the 12 items and a single latent categorical variable (with 2 classes) predicting the factor. My measurement model parameters (thresholds and loadings) are not allowed to vary across classes. I would like the factor means and variances of the two classes to vary. I thought I would need to fix a loading of an item to 1.0 and the mean of the factor in one of the classes to 0 for identification purposes. My results look odd, so I think I may be confused about how to specify the model in order for it to be identified and to ensure that I am interpreting the results correctly. Are there any other constraints that I need to make?

My model statement looks like so:
MODEL:
%overall%
f by q1* q2* q3* q4* q5* q6* q7@.1 q8* q9* q10* q11* q12*;

%c#1%
[f@0];
f;

%c#2%
[f];
f;
Thanks!
 Bengt O. Muthen posted on Thursday, August 03, 2006 - 4:59 pm
That looks like the right way of setting up the model, so for a further diagnosis you need to send the input, output, data, and license number to support@statmodel.com.
 Fiona Shand posted on Monday, February 22, 2010 - 7:30 pm
I have run a factor mixture model with 2 classes and 1 factor, with the factor means constrained to be zero and the thresholds free to vary across classes. All of my observed variables are dichotomous.Everything looks okay except I'm not getting the 'results in probability scale' for each class, so I don't know what the observed variable endorsement probabilities are for each class. I've set my model up as follows:

%OVERALL%
f BY u3-u13;
[f@0];
%c#1%
[u3$1-u13$1];
%c#2%
[u3$1-u13$1];

Thank you.
 Bengt O. Muthen posted on Tuesday, February 23, 2010 - 2:30 am
You can use the PLOT command to look at the probabilities for each item and class.
 Fiona Shand posted on Wednesday, February 24, 2010 - 2:52 am
The graphs are not quite what I need. I'm finding that when I use ALGORITHM=INTEGRATION, the model is identified but it doesn't give me the 'results in probability scale' for each class. If I don't use ALGORITHM=INTEGRATION, it gives me the 'results in probability scale' but the model is not identified. I'm not sure why using the INTEGRATION command prevents me from getting the item probabilities for each class. Thanks.
 Bengt O. Muthen posted on Wednesday, February 24, 2010 - 4:27 pm
You obtain the probabilities by requesting RESIDUAL in the OUTPUT command. These probs are obtained by numerical integration over the factor and are the ones shown in the PLOT.

Algorithm=integration is needed for a model with a continuous factor and categorical observed indicators.
 Fiona Shand posted on Wednesday, February 24, 2010 - 11:21 pm
Thank you, that has given me precisely what I needed.

Fiona
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