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Mplus Discussion > Latent Variable Mixture Modeling >
 EFried posted on Tuesday, June 19, 2012 - 4:06 pm
We are performing three individual LCAs at 3 measurement points (9 categorical items), and find the that a 3 class solution fits the data best at all measurement points. The classes look similar.

We want to perform a test of measurement invariance on these 3 classes over 3 measurement points now. However, we are unable to find examples of MPLUS syntax for this (neither in the videos/tutorials nor in the forum). Our understanding is that checking for measurement invariance is required in order to then perform LTA and predict class change by covariates.

Do you know of an example syntax? Or would you even recommend a different approach?

Thank you
 Linda K. Muthen posted on Wednesday, June 20, 2012 - 10:39 am
Measurement invariance is shown in Example 8.14, for example, by the equality of the thresholds. To test these equalities, use MODEL TEST. One should not do difference testing with mixtures because the classes will change.
 Stephan Junker posted on Wednesday, October 07, 2015 - 9:24 am
Dear All,
Iím doing a latent class analysis to differenciate between social classes. I have data from three different time points (2007, 2009, 2012). The data is from a panel study (Socio-Economic Panel, Germany).

Iím interested in testing if the latent categorical variable measures the same construct at the three time points and if the same classes are found. Iím not interested so far if the classes change in size or individuals change the classes or at least not to test if the changes are significant, (1) as I understand I need to do a Latent trait Analysis if I am interested in that, right?
In the moment Iím looking if I get the same number of classes for each time point and if they can be interpreted in the same way. In the next step (2) I wanted to do a multiple group LCA using the KNOWNCLASS Option with different equality constraints. Then use (3) Ďmodel testí, the Satorra-Bentler scaled chi-square difference test and -2(Difference between Logliklyhoods) as indicators for which type of measurement invariance can be assumed.

Is this the right approach so far or (4) is the KNOWNCLASS option only suitable for subgroups like countries or gender?
 Bengt O. Muthen posted on Wednesday, October 07, 2015 - 5:55 pm
1) No, you don't need latent trait analysis for that. You can use LTA.

2) If you thinking of time point as group that is not suitable for multiple-group/Knownclass analysis because the groups need to be independent, not the same people.

3) Model Test is fine.

4) See 2).
 Stephan Junker posted on Thursday, October 08, 2015 - 12:05 am
Dear Bengt O. Muthen,
thank you for your swift reply.

Unfortunately I have some follow up questions.

1) Sorry, I meant Latent Transition Analysis.

2) Is there a maybe a paper which explains why it is important to use dieffernt methods to look for measurement invariance over time and over subgroups you know of?

3) Does this mean the other two tests are not?

4) Do I need to use a LTA Model to test for measurement invariance over time?

Thank you very much!
 Bengt O. Muthen posted on Thursday, October 08, 2015 - 6:37 pm
2) That's a good question for SEMNET.

3) They are harder to carry out with mixtures because the more restrictive model throws off the class formation.

4) Yes.
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