Interpreating distal outcomes PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Daniel Rodriguez posted on Thursday, April 17, 2003 - 11:08 am
I ran a GMM with a distal outcome with three categories. The model ran well and I receive the expected outcome, including the latent class indicator model part in probability scale. Now, I have computed odds ratios. How can I tell whether my odds ratios comparing a given class probability to the reference class is significant? Where would I get the standard errors to compute a confidence interval? I'd appreciate your help greatly, as this is a question I anticipate a reviewer asking.
 Linda K. Muthen posted on Thursday, April 17, 2003 - 3:00 pm
I have a document that was prepared by another user that I can send to you that goes through this exercise. Email me at and I will send it to you.
 Rita posted on Monday, June 11, 2007 - 7:35 am
It seems that many people use LCA and there are studies including covariates and distal outcomes in the same model together with LCA. In different papers you could find various interpretations of such models (mediation, moderation, risk factors and outcomes). Basically it looks like mediation model, even though it is hard to interpret in that way.
How could you interpret such model, if there is a way to name it?
Let’s say you have a model where children’s temperament at age 3 (covariate) predicts parents behavior (that would be LCA) and both of them predict distal outcome – satisfaction with marriage at age 35. So, children’s temperament is a covariate and satisfaction with marriage – distal outcomes. In such model I have 3 classes or parents behavior and for each class I estimate distal outcomes.
How should I interpret this model, especially if the links between predictor and latent class is significant and in the same class the mean value of predictor is significantly higher compare to other classes? It is a mediation?
How should be interpreted if there is only one significant link between the covariate and distal outcomes for one class but not for others?
I would be grateful for you advice.
 Linda K. Muthen posted on Monday, June 11, 2007 - 9:58 am
In a model where the covariate x influences the categorical latent variable c which then influences a distal outcome u and you are interested in the relationship between x and u, I would call this mediation. This type of model has not been written about much in the latent class literature.
 Rita posted on Monday, June 11, 2007 - 10:13 am
Thanks a lot! I agree that is not much about that, but some people when talk about latent class or profile analyses with predictor and distal outcomes, refer as mediation model.
 Louise Lafortune posted on Thursday, July 10, 2008 - 8:07 am
I want to use a binary distal outcome to assess the predictive validity of my LCA results (4 classes; 6 categorical indicators).

I want to fix the class-specific item probabilities (i.e. values fixed at values from the 4 class model without covariates) to ensure the means are estimated based on classes I already have (re: I am referring to the strategy presented in K Nylun dissertation)

My model runs but I am not sure of my syntax. Here is what I have: I wrote the thresholds for the 6 categorical variables and did nothing for the distal outcome. The distal outcome just show up in the USEVAR ARE and CATEGORICAL statements.


USEVAR ARE cat1-cat6 distal;
CLASSES= c(4);
CATEGORICAL = cat1-cat6 distal;





Does this make sense?
 Linda K. Muthen posted on Friday, July 11, 2008 - 6:15 am
Can you point me to the page in the Nylund dissertation where it suggests fixing the values of the thresholds.
 Louise Lafortune posted on Friday, July 11, 2008 - 7:33 am
The information is on p.89, paragraph just below figure 3.2
 Linda K. Muthen posted on Friday, July 11, 2008 - 10:17 am
I see. This is one way of doing this. I would recommend not fixing the classes in this way. Although substantively you may think of the distal outcome differently than the latent class indicators, statistically the distal outcome is another latent class indicator. If this dramatically changes the classes, the reason for this should be investigated.
 Louise Lafortune posted on Friday, July 11, 2008 - 1:55 pm
I tried not fixing the classes and it does not substantively change the classes.
Thank you!
 Louise Lafortune posted on Tuesday, July 15, 2008 - 7:46 pm
Hi again,
I have an interpretation question. My 4 latent classes represent health status. I have age and gender as covariates and my distal outcome is mortality. In interpreting the ORs for the my distal outcome, is it correct to say that I've controlled for age and gender? For instance, the OR when comparing class 1 and class 2 is 4.5. Does it control for the age and gender differences between these classes as a multinomial regression would?

It may sound like a stat 101 question but I am not sure how Mplus takes care of the covariates in this case.
 Bengt O. Muthen posted on Wednesday, July 16, 2008 - 6:42 pm
The answer is yes. It works the same way as logistic regression.
 Philippa Clarke posted on Wednesday, July 29, 2009 - 1:46 pm
I'm using multiple distal outcomes in a GMM, allowing the means (thresholds) of the two distal outcomes to vary across classes as follows:


When looking at the effects of class membership on the distal outcomes (in the output), do the effects of class membership on one outcome control for the effects on the other outcome (i.e. are they adjusted effects)?
 Linda K. Muthen posted on Wednesday, July 29, 2009 - 4:40 pm
No, they are not adjusted effects. Note also that the conditional independence assumption applies to them. I would run the model with both distals and then with each distal and compare the results.
 Ginger Burrell posted on Friday, September 04, 2009 - 1:04 pm
I'm doing an LCA with a binary distal outcome and I'm not sure I understand how to interpret the output. The output excerpt below is from the 'Latent Class Odds Ratio Results' section. Am I correct in stating, based on this excerpt, that compared to Class 3, Class 1 is 2.179 times more likely to have an F1EVERDO score greater than category 1 than they are to have a score in category 2?

Latent Class 1 Compared to Latent Class 3


Category > 1 4.209 1.931 2.179 0.029
 Linda K. Muthen posted on Friday, September 04, 2009 - 4:52 pm
The first number is the odds ratio.

Compared to individuals in Class 3, individuals in Class 1 are 4.209 times more likely to have an F1EVERDO score greater than category 1 than they are to have a score in category 1.
 Lewina Lee posted on Wednesday, October 31, 2012 - 2:25 pm
Dear Drs. Muthen,

I'm running an LPA with 2 binary distal outcomes: DEAD & CHD. In the M+ output for a 2-class model, under "MODEL RESULTS" it lists the following thresholds right below the "Means" section:

(For class 1: )
CHD$1 0.919 0.105 8.790 0.000
DEAD$1 2.176 0.155 14.012 0.000

(For class 2: )
CHD$1 0.997 0.102 9.732 0.000
DEAD$1 2.067 0.143 14.408 0.000

How should they be interpreted?

Thank you for your help.

 Bengt O. Muthen posted on Wednesday, October 31, 2012 - 5:17 pm
The thresholds are the negative of logit intercepts, so that for a given class

P(distal=1) = 1/(1+exp(threshold)).

That gives the interpretation.
 Lewina Lee posted on Thursday, November 01, 2012 - 12:02 pm
Thank you!
 Mary Mitchell posted on Wednesday, December 18, 2013 - 11:01 am
Dear Drs. Muthen,

I ran a model with a binary distal outcome and am not sure how to interpret it. I got a mean of -2.33. Is the scale interpretable? Does this mean that C#1 has a sig lower mean that C#2 on the outcome?

 Bengt O. Muthen posted on Wednesday, December 18, 2013 - 11:12 am
It sounds like you have a mixture model for which a binary distal has a threshold parameter estimate for each class. The thresholds are related to the probability of the distal. The threshold differences can be tested for significance and so can the probabilities - you would use Model Constraint to do this.
 Mary Mitchell posted on Wednesday, December 18, 2013 - 8:25 pm
Dear Dr. Muthen,

Thank you so much for your explanation - that the thresholds and thus, the probability of the distal outcome varies significantly between the two classes. Would model constraint tell me that the two classes have sig different probabilities or would it also tell me which class was higher (and the magnitude)?
 Mary Mitchell posted on Thursday, December 19, 2013 - 8:10 am
Dear Dr. Muthen,

Looking at my output further, I found:


CERTAINA32 (my binary outcome)
Mean S.E.

Class 1 0.387 0.036
Class 2 0.589 0.119

Chi-Square P-Value

Overall test 2.549 0.110

So, this output suggests that there really is no significant difference in means of the outcome variable across the two classes, right?


 Bengt O. Muthen posted on Thursday, December 19, 2013 - 1:30 pm
Are you using the Auxiliary option "e" for your binary distal, that is, a 3-step run, or are you doing a 1-step run? Perhaps you'd better send your output to Support.
 Lauren Cole posted on Wednesday, February 11, 2015 - 9:08 am
I am trying to use the manual 3-step approach for my dissertation work. I am having trouble with the third step, where I am trying to regress a binary distal outcome on a categorical latent class variable (5 classes) while controlling for covariates. I am getting an error that my model statements are ignored. Any help would be greatly appreciated (see code below).

Also, I see that in other responses on the message boards Drs. Muthen have said that ‘Variables cannot be regressed on the categorical latent variable. This effect is found in the means of the variables varying across classes.’ Even if I can figure out how to get my model to run, will I be able to get the odds ratios for the relationship between the latent classes and the distal outcome? THANKS!

Here is my code:



 Bengt O. Muthen posted on Wednesday, February 11, 2015 - 6:08 pm
You should declare your distal as categorical. You should replace




You get the odds ratios by labeling the thresholds for the distal and using Model Constraint to express the distal probabilities and the odds and odds ratios. See our Topic 6 handout, slide 151 for an example with formulas for this.
 Lauren Cole posted on Friday, February 13, 2015 - 1:13 pm
Thank you so much for your response, Dr. Muthen! It was very helpful and I have been able to get my models to run, but I still have a question about labeling the thresholds for the distal outcome and using Model Constraints to express the distal probabilities. I am not familiar with Model Constraints and have consulted the User's guide, but I am still not sure how to use the constraints to obtain the odds ratios. I tried a few things, but none of it would work. Could you give me an example or direct me to an appropriate handout that could help me figure out this step? Thank you!
 Bengt O. Muthen posted on Friday, February 13, 2015 - 1:37 pm
You give labels to the threshold of the distal in each class in the Model command, so for 3 classes assuming a binary distal:

[distal$1] (d1);
[distal$1] (d2);
[distal$1] (d3);

and then in Model Constraint you say, following slide 151 of the Topic 6 handout:

New(prob1 prob2 prob3 odds1 odds2 odds3 or13 or23);
prob1 = 1/(1+exp(d1));
prob2 = 1/(1+exp(d2));
prob3 = 1/(1+exp(d3));
odds1 = prob1/(1-prob1);
odds2 = prob2/(1-prob2);
odds3 = prob3/(1-prob3);
or13 = odds1/odds3;
or23 = odds2/odds3;
 DavidBoyda posted on Thursday, December 28, 2017 - 11:05 am
Dear Dr. Muthen,

I am seeking to obtain odds ratios for my distal outcome (Y) and examining the above, have labelled the threshold for the distal using model constraint. I have run the model with no errors (I think), but I am unsure where the odds ratios for Y are printed in the new output.
 Bengt O. Muthen posted on Thursday, December 28, 2017 - 12:58 pm
These odds ratios are not printed but are obtained as discussed in Section 3.2 of the paper on our website:

Muthén, B., Brown, C.H., Masyn, K., Jo, B., Khoo, S.T., Yang, C.C., Wang, C.P., Kellam, S., Carlin, J., & Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3, 459-475. Mplus inputs and outputs used in this paper can be viewed and/or downloaded from the Examples page.
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