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?
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.
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.
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?
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? Thanks.
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
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.
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: %c1#1% [i1]; %c1#2% [i1];
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.
Thank you very much for the suggestion and reference.
When trying to run with BCH, I get the error:
*** ERROR in VARIABLE command Auxiliary variables with E, R, R3STEP, DU3STEP, DE3STEP, DCATEGORICAL, DCONTINUOUS, or BCH are not available with TYPE=MIXTURE with more than one categorical latent variable.
Is there an error in my coding, or if not, any suggestions to get around this restriction?
If I have a model based off of two categorical latent variables, is there any another other way to estimate and test differences in auxiliary variables across groups other than the auxiliary functions?
I have analyzed two different types of second-order growth mixture models using Mplus. One approach was built based on multiple indicator growth model(example 6.14 of Mplus manual; Curve-of-Factors Approach). I have seen that most literatures have used this model as a measurement model of second-order growth mixture model. However, I detected many convergence problems(e.g., negative variances, or local maxima) when I used this approach.
Thus, I am now considering another approach which has been known as Factor-of-Curves model (Duncan's 2006 Growth Curve Model book). This approach estimates common growth factors using multiple growth factors instead of multiple manifest indicators. When I used this model as a measurement model of Second-order growth mixture model, I found that the model has less problems compared to curve-of-factors approach and reduced computational time. However, I had never seen this type of Second-order growth mixture model. So, I am not sure whether I can use a factor-of-curve latent growth curve model as a measurement model of second-order growth mixture model.
Therefore, I would like to ask you for your advice if second-order growth mixture model can be built based on factor-of-curves latent growth curve model. Also, could you let me know if there is any relevant paper in this area? I am more than grateful for your advice.
Both approaches can be used with growth mixture modeling. The choice depends on which factor means you want to vary across your latent classes. One model may be more parsimonious than the other and may not fit as well. Note that often more flexible, less parsimonious, better-fitting models can perform worse in terms of convergence, negative variances, etc. I am not aware of articles on this, but perhaps others are?
Dear all, we just performed a LCA model with cross-sectional data regarding 12 dichotomous symptoms.
With the results in hands, it seems that a best solution would be some sort of "intermediate" model between 2 and 3 latent classes, since graphics have shown a huge convergence in 6 of the 12 symptoms in the 3-class model.
Our questions are:
1) It would be possible to perform a second-order LCA model with first-order 2 classes and some second-order classes (from one of the first-order classes) as follows:
Class 2 --> Class 2-a --> Class 2-b --> Class 2-Etc.......
2) If yes, would you mind indicating us how the MODEL syntax for that would be?
Perhaps 3 classes would not be needed (in terms of BIC) if you added some residual covariances among your class indicators in the 2-class model. See the paper on our website:
Asparouhov, T. & Muthen, B. (2015). Residual associations in latent class and latent transition analysis. Structural Equation Modeling: A Multidisciplinary Journal, 22:2, 169-177, DOI: 10.1080/10705511.2014.935844
Otherwise, you can try to formulate any latent class model you want using "confirmatory LCA" - see our UG ex 7.13 and 7.14.