LCA with effects between indicators a... PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Anonymous posted on Tuesday, October 31, 2000 - 4:16 pm
I have two questions about performing analyses with categorical latent variables.

First, is there a convenient way to specify direct effects between indicators in Mplus ? I have tried modeling one of my indicators as a separate covariate but without any success. Could you provide an example of suitable Mplus code ?

Second, my understanding is that by incorporating a path between a covariate (say, gender or income) and an indicator variable (IV) in a latent variable (LV) model one can "correct" for DIF in the final model. My question is then how one should interpret the coefficient between the covariate and the latent variable in such a situation since the effect of gender (or income) would appear to be attenuated by the effect of the covariate on the indicator variable. Does one simply consider the effect on the LV regardless of its effect on the IV, or is there some standard way of taking the effect of the covariate on the IV into account in judging its effect on the LV ?
 bmuthen posted on Wednesday, November 01, 2000 - 10:10 am
Here is an example with two factors:

f1 by y1-y5;

f2 by y6-y10;

f2 on f1 x;

!below is the direct effect you request:

y10 on y2;

Regarding your second point, I think your understanding is correct. First, one can correct for DIF in this way. Second, you do simply consider the effect of the covariate on the LV; note that this effect will be different when including the direct effect DIF as compared to when not including it.
 CB posted on Monday, October 06, 2014 - 7:12 am
I'm conducting LCA, but I am interested in adding an exogenous variable to only have a direct effect on an indicator variable. Is this possible to do in MPlus? If so, how would I code this additional direct effect? Additionally, I imagine that this would simply be interpreted as the effect of the exogenous variable on the indicator, but I'm unsure about what this estimate would be called other than this direct effect (as it's neither a latent class probability nor an item-response probability).
 Bengt O. Muthen posted on Monday, October 06, 2014 - 7:56 am
You would simply say

u ON x;

where u is the latent class indicator and x is the exogenous variable. This implies measurement non-invariance wrt x, that is, subjects in the same class differ in their response probability for u as a function of the x values.
 CB posted on Wednesday, November 26, 2014 - 1:43 pm
I'm conducting LCA and I understand how to code the direct effect of an exogenous variable onto an indicator that has three levels. How is this effect interpreted, especially in the output?

Also, for another analysis, I will be conducting LCA with a covariate predicting the 2-class latent variable. I also plan on looking at the effect of this covariate onto one of the indicators. Does this violate the conditional independence assumption and/or does it just mean that there is measurement non-invariance? Will this effect be interpreted the same as the effect of an observed exogenous variable on an indicator?

 Bengt O. Muthen posted on Wednesday, November 26, 2014 - 6:19 pm
Q1. This is interpreted the same as logistic regression with an ordinal DV.

Q2. It means that you have measurement non-invariance. It is ok to violate conditional independence as long as the model is identified. Here you still have independence among the indicators if you have a direct effect on to only one indicator.

Q3. You want to have the exogenous variable influence the latent class variable in both models: It is an unusual model that has only a direct influence and not the indirect one via the latent class variable.
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