Second-Order Latent Class Model PreviousNext
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 Scott Eliason posted on Tuesday, September 12, 2006 - 1:52 pm
Hi Folks,

This is my first post, and so please excuse any normative slip-ups on my part.

We would like to estimate a Second-Order Latent Class Model, with a mix of categorical/nominal observed indicators and categorical/nominal latent variables on the first and the second order. Graphically, the model looks exactly like the model in example 5.6 of the Mplus manual, but with all categorical/nominal variables instead of the continuous observed and latent variables given in the example.

Our question is, what's the most efficient Mplus code to achieve this type of latent class model?

Any and all help is greatly appreciated. Thanks!
 Bengt O. Muthen posted on Sunday, October 01, 2006 - 12:33 pm
Second-order LCA has the flavor of UG ex 8.14 but without c2 on c1 and without the observed indicator (threshold) restrictions. For the second level, you would have the Overall model with c1 on c and c2 on c. For the first level you would have a Model c1 and a Model c2. Look at Tech1 to see that you get what you want.
 Matthew Cole posted on Wednesday, July 11, 2007 - 10:30 am
Hi Folks,

Is this example (8.14) the place I should start if I want to run a multiple indicator GMM, similar to example 6.14?

I've got longitudinal data that doesn't quite provide the complete picture if its reduced to one factor, so I'm wondering if I can run (or if I should even consider running) something akin to a multiple indicator GMM.

Also, my data is cluster randomized, so I'm going to be analyzing it in a multilevel context after I've completed the first step of the single level analysis.

 Linda K. Muthen posted on Wednesday, July 11, 2007 - 5:07 pm
You should start with the one class model in Example 6.14. Then estimate it for two classes etc. by adding TYPE=MIXTURE; to the ANALYSIS command and the CLASSES option to the VARIABLE command.
 Matthew Cole posted on Wednesday, July 11, 2007 - 6:05 pm

I have another question regarding LCA and a different data set.

I have data of 7 binary drug and sexual risk behaviors at baseline, immediate post-intervention, 6 months, and 12 months. The LCA at baseline found a 3-class solution.

I would like to look at the three subpopulations found at baseline and see how they responded to the intervention. I guess one approach would be to simply run growth models in each subpopulation on each risk behavior one after the other. Or I could do the multiple indicator growth model as a multiple group growth analysis.

Is there another approach you can recommend where I could do all of this in one step?
 Bengt O. Muthen posted on Wednesday, July 11, 2007 - 6:28 pm
If your 7 binary indicators are well summarized by 3 latent classes, perhaps you would be interested in seeing how subjects transition between those classes over time and how those transitions are affected by the intervention. If so, Latent Transition Analysis is suitable. We can send more information about Mplus input for intervention analysis if this is where you want to go.

You mention growth modeling in each of the 3 classes, which sounds like you think there is variation across people within classes. If that's the case, perhaps LCA is not the best measurement model, but instead Factor Mixture Analysis (not imposing measurement invariance across classes). As an advanced approach, an FMA measurement model can be used for a combined growth and transition analysis.

As yet another alternative, you can see the 7 binary items as indicators of a (say) single continuous factor, where this factor has 3 classes and you use that factor as your dependent variable in a GMM - that is then a multiple-indicator GMM. Its measurement model can be seen a Mixture Factor Analysis (class-invariant measurement parameters).
 Mplususer  posted on Wednesday, January 30, 2008 - 4:56 pm
Hi there,
Following your response to Matthew Cole on July 11, I have a question about multiple-indicator GMM. Suppose we have scores for 7 items across 3 time
points and we don't know if they are all loaded on the same factor across
time. Do we need to run factor analyses at each time point to preliminarily examine if the items are loaded on this factor, and then use the factor scores as the values of a dependent variable for GMM analysis? Is Example 6.14 still the place to start the analysis?
 Linda K. Muthen posted on Thursday, January 31, 2008 - 11:11 am
You need to check for measurement invariance across time. Example 6.14 without the growth model is the place to start. I would then continue with a multiple indicator growth model. I would not use factor scores with less than 15 factor indicators.
 Mplususer  posted on Thursday, January 31, 2008 - 11:50 am
Thanks, Linda!
 Shawn Latendresse posted on Friday, February 04, 2011 - 11:55 am
With respect to the second-order LCA described in Bengt's 10/1/06 response (above), can this be extended to the case where c1 and c2 are both GMMs?
 Bengt O. Muthen posted on Friday, February 04, 2011 - 3:25 pm
I think you mean that c1 and c2 are latent class variables influencing growth factor means for GMMs. Yes, that kind of second-order LCA is possible to do in Mplus.
 Shawn Latendresse posted on Saturday, February 05, 2011 - 3:05 pm
No, actually the other way around, where the second order latent class variable (i.e., the c in example 8.14) is a function of two latent categorical variables, c1 (externalizing trajectory class) and c2 (internalizing trajectory class). If this is possible, I seem to be having a problem figuring out how to specify it in the model statements. Specifically, I keep getting error messages indicating that all growth factors need to be specified in the overall statement. However, in the model I'm describing, there are growth factors specific to the c1 and c2 models, but not second order latent class variable. I'd appreciate any help you can offer. Thanks.
 Bengt O. Muthen posted on Sunday, February 06, 2011 - 12:22 pm
Seems like you can give the two growth models in the Overall part and then in the c-specific parts mention the class-specific growth factor means for the respective growth model. So like:

Model c1:

and the same for Model c2 using [i2] (and other growth factor means. This implies that [i1] is held equal across the c2 (and c) classes, and so is only a function of c1 classes. And analogously for [i2].

Check in Tech1 that you get the equalities you need.

That's quite a complex model.
 Shawn Latendresse posted on Tuesday, February 08, 2011 - 11:27 am
Thanks so much! The model runs beautifully.
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