Categorical and continuous indicator PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
Message/Author
 Seungbin posted on Wednesday, June 02, 2004 - 9:30 am
Is it possible to have both categorical and continuous indicators in one mixture model?
I just used "categorical" command to add categorical indicator, but there was error message.
Thank you.
 Linda K. Muthen posted on Wednesday, June 02, 2004 - 9:55 am
You can have both. Send the output with the error message to support@statmodel.com.
 Silvia S Martins  posted on Thursday, July 05, 2007 - 8:26 am
I am running a LCA with both binary (categorical) and nominal indicators (unordered). How do I interpret the LCA results for the nominal indicators? I get means for each nominal category intstead of thresholds. How do I compare results from nominal indicators across different classes? Is it possible to get Odds Ratios for them?

Thanks
 Linda K. Muthen posted on Thursday, July 05, 2007 - 9:39 am
They are logits. You can turn them into odds ratios or probabilities. See Chapter 13, Calculating Probabilities for Logistic Regression Coefficients. The example with all covariates at zero would apply.
 Peter Cabrera-Nguyen posted on Thursday, September 23, 2010 - 6:21 pm
I apologize if I am about to assault you with a barrage of stupid questions, but I am relatively new to latent class models.

I realize that LCA uses categorical indicators whereas LPA uses continuous indicators. Also, I am aware that LPA makes the "strong" assumption that covariates temporally precede the latent categorical variable.

My dilemma: I specified a LC model with 4 indicators: 3 indicators have ordered categorical response options, and the other indicator is continuous. I was able to determine the # of latent classes w/ ease, and the baseline latent class solution has excellent entropy.

Would this be more aptly classified as a LPA instead of a LCA even though it has only one continuous indicator? Or is there a more appropriate name for this type of model? If it is not a true LPA, would this model also include the assumption that covariates temporally precede the latent categorical variable (given the continuous indicator)?

Incidentally, recoding the continuous variable into a categorical variable would not be a theoretically sound strategy in this case.

Thanks in advance for your assistance.
 Linda K. Muthen posted on Thursday, September 23, 2010 - 6:46 pm
I would call this an LCA with a combination of categorical and continuous latent class indicators. There is no difference between LCA and LPA regarding covariates.
 Marinka Willemsen posted on Thursday, May 07, 2020 - 8:01 am
Dear all,

I am conducting a LPA with both continuous indicators (10 of them) and categorical indicators (2 of them). I understood this combination is perfectly possible, yet I have some difficulties with the difference in output since I am only familiar with a LPA with continuous indicators. I wonder about some differences:

1. Model fit information: no CFI/TLI/RMSEA,
can I still request these? If no, what is the alternative?

2. The difference between: (what do you use for what?)
(a) the thresholds in the model results
(b) results in probability scale
(c) latent class odds ratio results

3. Requesting plots and using them in the report: I know that I can define two different plots in the syntax, but is there a way to still combine them? How would you report the profiles if the categorical ones are excluded in the graphical representation?

4. Interpretation of a significant categorical indicator

Any example of a LPA with both categorical and continuous indicator would also be of great help.

Thank you,
 Bengt O. Muthen posted on Friday, May 08, 2020 - 9:28 am
1. No the usual SEM fit information is not available here because the usual sample statistics are not sufficient. You can use TECH10 for the categorical indicators.

2.(a) I don't consider the thresholds unless I want to translate them into probabilities.

(b) that's a good way to interpret categorical outcomes.

(c) ORs are also useful

I would use b and c in combination. Web Note 13 discusses both in the context of the related LTA model.

3. No, Mplus does not provide a combination of mean plots for continuous outcomes and probability plots for categorical outcomes. But Mplus can plot them separately and there is an option to save the information used in the plot so you can plot them yourself in some fashion.

4. I don't know what that means. I don't use such a terminology.

There are people who use a combination of scale types for the outcomes but I can't point to papers on that. You can check on our Papers page under LCA and also ask on SEMNET.
 Marinka Willemsen posted on Monday, May 11, 2020 - 3:00 am
Dear Bengt,

Thank you for your reaction and the information.
 Marinka Willemsen posted on Monday, May 11, 2020 - 7:00 am
Two questions still about TECH10.

(1) I read up about the response patterns provided by TECH10 in Geiser (2012), but I am still not sure how to interpret the UNIVARIATE (AND BIVARIATE) MODEL FIT INFORMATION; how do I interpret these?

(2) And is there nothing to be said/retrieved about the model fit of the continuous indicators?
 Bengt O. Muthen posted on Monday, May 11, 2020 - 2:06 pm
(1) The bivariate info is the more important. It gives standardized residuals so you want to see where you get significant ones (say > 2). Also see how we use this info in the crime count example in the paper on our website:

Muthén, B. & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussian random effects. In Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.), Longitudinal Data Analysis, pp. 143-165. Boca Raton: Chapman & Hall/CRC Press.
download paper contact first author show abstract

(2) You can request Residuals.

Typically, BIC is used to choose models but that gives only relative fit of several models not absolute fit so you are right to explore this.
 Marinka Willemsen posted on Tuesday, May 12, 2020 - 7:40 am
Thank you for the quick reply.

(1) Interesting crime count example. In my output for the 3 profile solution, which seems the best on the basis of BIC, there are no significant ones (highest is .9). Yet neither did the other profile solutions showed significant residuals (2-5 profile solutions).

(2) Can I interpret these residuals in the same way as the above? I see the column Stand. Residual, that's also the z-score right?

BIVARIATE DISTRIBUTIONS FIT FOR CLASS 2

Variable Variable Observed Estimated Residual (Obs.-Est.) Stand. Residual
GENDER EDUEDU
Category 1 Category 1 0.020 0.013 0.007 1.441
Category 1 Category 2 0.055 0.062 -0.007 -0.666
Category 2 Category 1 0.147 0.156 -0.009 -0.532
Category 2 Category 2 0.778 0.769 0.009 0.458
 Bengt O. Muthen posted on Tuesday, May 12, 2020 - 5:43 pm
1) That's an unusual result.

2) Yes.
 Marinka Willemsen posted on Wednesday, May 13, 2020 - 7:10 am
1) could it be explained by the high entropy? (0.998)

And perhaps interesting for this forum: A SEMNET contribution provided me with the following article (potentially interesting for the ones interested in the use of both categorical and continuous indicators):

Morgan, G. B. (2015). Mixed mode latent class analysis: An examination of fit index performance for classification. Structural Equation Modeling, 22(1), 76–86. https://doi.org/10.1080/10705511.2014.935751
 Bengt O. Muthen posted on Wednesday, May 13, 2020 - 10:11 am
1) Such a high entropy is peculiar. It seems like some variables define the classes almost exactly e.g. with only 1 value in each class.

2) What is lacking in that article is discussing fit to the data. It talks about relative fit (AIC, BIC etc) among competing models - but the models can all fit the data poorly. TECH10 is an example of checking fit to the data.
 Marinka Willemsen posted on Thursday, May 14, 2020 - 2:22 am
1) I explored your suggestion, and yes something like you describe is the case. For class 1 three different values are found, class 3 two different values (but quite skewed towards one value), and yes for class 2 there is only one value found - and that's the biggest class. Thus, not exactly only one value in each class, but close to it. Whenever I substitute the indicator with a substantively different indicator, the entropy decreases a lot. Yet when I use a similar indicator in terms of meaning (as the first), the same happens as before. These kind of indicators seem to have a dominance in the profiling.

Still, the indicator is of substantive importance in the model, thus I am still hesitant about omitting it. Could it be a solution to describe the role of this indicator in the profiling?

2) Definitely a good point.
 Bengt O. Muthen posted on Thursday, May 14, 2020 - 3:44 pm
No need to omit that indicator. Just discuss this as you say. Perhaps a smaller number of indicators is sufficient. Note also that you can get indicator-specific entropy values. See our technical appendix for Version 7:

Variable-specific entropy contribution.
 Marinka Willemsen posted on Friday, May 15, 2020 - 7:17 am
Thank you, that's a great addition.

Kind regards,
Back to top
Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action: