LCA with distal outcome? PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Jennifer Moren Cross posted on Friday, May 25, 2007 - 8:43 pm
1) Is it possible to estimate LCA with a distal outcome in a single step in Mplus(along the same lines one does with LCGA or GGMM)? (Are there examples of this anywhere?)

2) Would I obtain the same results if I used a two-step procedure whereby, first, I estimated conditional latent classes with covariates (while also identifying my distal outcomes using the "auxillary" command), export this to another statistical package like Stata, and second, run regular regressions of my distal outcomes on class probabilities in Stata?

Much thanks for any information!
 Linda K. Muthen posted on Saturday, May 26, 2007 - 6:31 am
1. Yes. It would be like Example 8.6 but with an LCA model instead of a GMM model.

2. It is always preferable to do the entire model estimation in one step. Doing it in two steps would introduce estimation errors and the standard errors will be incorrect.
 Jennifer Moren Cross posted on Saturday, May 26, 2007 - 11:04 am
Thank you, Linda. Are there any references you would recommend for me to read more about this type of estimation error? Thanks!
 Linda K. Muthen posted on Monday, June 04, 2007 - 11:10 am
I don't know of any specific reference. Perhaps you could find something in a general statistical text.
 Michelle Maier posted on Thursday, March 03, 2011 - 8:57 am
I am running a LCA with several covariates and distal outcomes. I would like to control for the distal outcome scores in the fall so I have specified "outcome on fallscore" in my overall model. Because of this, I get intercepts for my distal outcomes instead of means. I have two questions:

1) What is the best way to request the class means for the outcomes? Tech7?

2) What is the best way to compare my 3 classes on the distal outcomes? I have used MODEL TEST but isn't that comparing the class intercepts and not the means in my particular model?

Thank you in advance for your time!
 Linda K. Muthen posted on Friday, March 04, 2011 - 11:06 am
1. TECH7 is sample statistics. TECH4 and the RESIDUAL option of the OUTPUT command give model estimated values.

2. You would need to define the means in terms of the model parameters using new parameters in MODEL CONSTRAINT where you can also test the differences.
 Keri Jowers posted on Tuesday, September 20, 2011 - 12:08 pm

I'm aiming to use LCA to predict both categorical and continuous distal outcomes. From what I see in Example 8.6, it seems like the current recommendation is to basically do the equivalent of including it as a covariate (c on x). Is that the correct interpretation?

If so, when I do that, the size of my 3 class shift more than I'd expect or like for them to (even when I've specified the stat values for each of the latent class indicators. My understanding is that this indicates that the model may be unstable or not replicable, and that the number of classes may not be correct. The 2- and 3-class models have very similar fit indices:

2-class (79.14%, 20.86%):
AIC = 4431.098
BIC = 4498.885
SSABIC = 4451.258
LMR-adj LRT p = .0007
BLRT p = .0000
entropy = .789

3-class (47.31%, 31.33%, 21.36%):
AIC = 4400.205
BIC = 4504.146
SSABIC = 4431.146
LMR-adj LRT p = .0378
BLRT p = .0000
entropy = .720

The 3-class model is a better fit theoretically/substantively. What, then, is the best way to estimate the association between the latent classes and the distal outcome? Can I trust the results I get when the classes are shifting?

Thanks so much in advance for your input!
 Bengt O. Muthen posted on Tuesday, September 20, 2011 - 6:51 pm
In ex 8.6 the distal outcome is u, not x.
 Keri Jowers posted on Wednesday, September 21, 2011 - 10:43 am
Apologies -- I mistyped. So, in ex 8.6, the distal is mentioned only in the "categorical = u" statement. How would one estimate the association between the latent classes and a continuous distal?
 Linda K. Muthen posted on Wednesday, September 21, 2011 - 11:14 am
The key is that u is on the NAMES list so it is an analysis variable. In the case where all variables on the NAMES list are not analysis variables, u would have been on the USEVARIABLES list. The same holds for a continuous distal outcome. It needs only to be on NAMES or NAMES and USEVARIABLES.
 Keri Jowers posted on Thursday, September 22, 2011 - 11:49 am
Right, I've got the NAMES and USEVARIABLES piece. Perhaps a better way of posing my question is this: When the continuous distal is in the USEVARIABLES list and I then set the start values for my LC indicators (not the u) using my previously obtained thresholds to try to preserve my classes, the output provides me with class-specific means for the distal, and these are based on the re-estimated model I mentioned above. Are these means and their associated p-values intended to be interpreted as the association between the latent class and the distal? This seems counterintuitive to me.
 Linda K. Muthen posted on Thursday, September 22, 2011 - 1:16 pm
The relationship between the categorical latent variable and the distal is found in the varying of the means of the distal across classes. The question you want to ask is if these means are the same across classes or different. You can use MODEL TEST to answer this question.
 Keri Jowers posted on Friday, September 23, 2011 - 8:07 am
Thanks so much! One final question -- how concerned should I be that the class sizes change drastically when compared to when the distal is not included in the USEVAR statement? Not only are the class proportions very different (below), but the sample proportions within each class are very different:

without distal in USEVAR:

with distal in USEVAR:
 Linda K. Muthen posted on Friday, September 23, 2011 - 9:45 am
When you add a distal outcome, it is the same as adding another latent class indicator. The classes will be affected by this. This means that the distal is being taken into account which it should be.
 Debbie Hahs-Vaughn posted on Monday, February 27, 2012 - 7:58 pm
We have estimated a six-class solution in LPA and are interested in using the LPA class membership (which was estimated at Time 1) to predict a distal outcome (at Time 2) while controlling for various attributes at Time 1. I recently attended a conference and heard a presentation that discussed "distal-as-consequence" where class membership is treated as missing data in the regression of the distal outcome on class membership and multiple imputations are used based on the posterior class probabilities (obtained from the estimated growth mixture model without the distal outcome included) to estimate the association between class membership and distal outcomes.

I have searched the Mplus archive and reviewed papers posted as well as the manual for more information/examples on this. Thus far, I have not found any. Any suggestions? Thank you.
 Bengt O. Muthen posted on Monday, February 27, 2012 - 8:14 pm
Section 4 of this paper on our web site discusses plausible values for latent class variables obtained by multiple imputation and how those plausible values can be used:

Asparouhov, T. & Muthén, B. (2010). Plausible values for latent variables using Mplus. Technical Report.
 C. Gantz posted on Monday, February 02, 2015 - 7:48 pm
I have read with great interest the many posts on using LCA to predict distal outcomes. I understand this is a complex topic.

In my analysis, I would like to use a 3 class solution at T1 to predict a variety of T2 continuous outcomes. I additionally would like to control for T2 outcomes at T1. In the first step of this analysis, a three class solution was best based on AIC, BIC and Lo-Mendell, with entropy of .89. These three classes also make a lot of sense theoretically.

My question is as follows:

I understand that often the one step approach is preferable here. However, I read the Clark & Muthen (2009) piece, and it seems that when entropy is high, it is acceptable to use the most likely class membership. When I included the outcome in the class estimation, this significantly changed the formation of the latent classes in a way that no longer made theoretical sense. Am I right to interpret the Clark & Muthen (2009) paper that in this case, given the high entropy from my 3 class results, I could be justified to assign most likely class membership and use these in follow up analyses?
 Bengt O. Muthen posted on Tuesday, February 03, 2015 - 10:26 am
 C. Gantz posted on Tuesday, February 03, 2015 - 10:32 am
Thank you so much for your quick reply, Bengt!
 C. Gantz posted on Tuesday, February 03, 2015 - 10:40 am
Apologies, one quick follow up here: The Clark & Muthen paper appears to be unpublished - is this the case? If so, do you happened to have a reference to this line of logic in a published paper?

Thank you!
 Linda K. Muthen posted on Wednesday, February 04, 2015 - 9:54 am
You can open the data file with any Mac text editor.
 Bengt O. Muthen posted on Wednesday, February 04, 2015 - 11:02 am
I think you can refer to the paper below for this logic:

Asparouhov, T. & Muthén, B. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 21:3, 329-341. The posted version corrects several typos in the published version. An earlier version of this paper was posted as web note 15. Appendices with Mplus scripts are available here.
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