LCA with effects between indicators a...
Message/Author
 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?

Thanks!
 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.
 Anna Hawrot posted on Thursday, January 29, 2015 - 7:00 am
Hello, I was trying to verify measurement invariance (MI) across gender of a 5 class LCA solution with binary and ordered categorical indicators. I followed Kankaras, Moors and Vermunt (2010)* procedure which uses covariate specification. The analyses showed that MI didn't hold for two items and in consequence, it was necessary to add two direct effects. I'm pasting the model part of my syntax to make sure it's clear what I mean. There were only slight shifts between classes after adding gender as the covariate.

MODEL:
%overall%
c on gender;
item1 on gender;
item5 on gender;

Is it possible to take into account this kind of non-invariance while using BCH method? I'd like to use BCH method to prevent class shifts in models with gender and other auxiliary variables and/or distal outcomes.

* Kankaraš, M., Moors, G., & Vermunt, J. K. (2010). Testing for measurement invariance with latent class analysis. In: E. Davidov, P. Schmidt, J. Billiet, (Eds.), Cross-cultural analysis: Methods and applications, pp. 359-384. Routledge.
 Tihomir Asparouhov posted on Thursday, January 29, 2015 - 2:13 pm
Yes
 Anna Hawrot posted on Thursday, January 29, 2015 - 2:19 pm
Could you, please, give an example syntax? I've tried to do that but with no success.
 Tihomir Asparouhov posted on Thursday, January 29, 2015 - 3:22 pm
Here is a simulation - you can run this in Mplus. In a non-simulation example you have to take the X variable out of the model.

___________________________

Montecarlo:
Names are U1-U5 x g;
Generate = U1-U5(1);
Categorical = U1-U5;
Genclasses = c(2);
Classes = c1(2);
Nobservations = 500;
Nrep = 10;
Auxiliary = x(bch);

Analysis: Type = Mixture; estimator=ml;

Model Population:
%Overall%
x*0.1; g*1;
C#1 on g*1;
U1 on g*1;

%c#1%
[U1\$1-U5\$1*-1.0];
[x*-1];
U1 on g*1;

%c#2%
[U1\$1-U5\$1*1.0];
[x*1];
U1 on g*-1;

Model:
%Overall%
[x] (1);
x (2);
C1#1 on g*1;
U1 on g*1;

%c1#1%
[U1\$1-U5\$1*-1.0];
U1 on g*1;

%c1#2%
[U1\$1-U5\$1*1.0];
U1 on g*-1;
 Anna Hawrot posted on Friday, January 30, 2015 - 1:47 am
Thank you for your prompt response. I tried to translate your example into my syntax, but apparently I don't fully understand your syntax. Here is one of my syntaxes (I have a few more, but none of them worked).

DATA:
FILE IS bch_weights.csv;
VARIABLE:
NAMES ARE x1-x7 gender w1-w5 mlc id;
USEVARIABLES ARE gender w1-w5 x1 x5;
CATEGORICAL ARE x1 x5;
MISSING ARE *;
CLUSTER IS id;
CLASSES = c (5);
training = w1-w5(bch);
ANALYSIS:
TYPE IS complex mixture;
STARTS = 0;
MODEL:
%overall%
c on gender;
x1 on gender;
x5 on gender;

I'm still getting the message:

THE LOGLIKELIHOOD DECREASED IN THE LAST EM ITERATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.

What am I doing wrong?
 Linda K. Muthen posted on Friday, January 30, 2015 - 7:05 am
 Tihomir Asparouhov posted on Friday, January 30, 2015 - 8:41 am
Anna you should use the automatic BCH approach, see page 5 of
http://statmodel.com/examples/webnotes/webnote21.pdf
Just one run, no training weights. Just add the whole model to that example including this part

MODEL:
%overall%
c on gender;
x1 on gender;
x5 on gender;
 Anna Hawrot posted on Friday, February 06, 2015 - 3:59 am
Tihomir, thank you a lot. I can't believe it's so simple! However, I'm still not sure whether it is what I want to do. As far as I understand form WN No. 21, the automatic procedure doesn't allow to estimate more complex models (e.g., predictors & distal outcomes in the same model). As I'm interested in the complex ones, the automatic procedure is not for me.

My idea how to "correct" my LCA model for DIF and use this "correced" model later is as follows:

BCH manual procedure, step 1: as in WB No. 21 + in the model part:
MODEL:
%overall%
x1 on gender;
x5 on gender;

BCH manual procedure, Step 2: as in WB No. 21, including "c on gender" command (and other class membership predictors) in the model part.

Does it make sense to you?
 Tihomir Asparouhov posted on Friday, February 06, 2015 - 9:53 am
This sounds good to me.
 Anna Hawrot posted on Wednesday, February 11, 2015 - 3:06 am
Thank you for all your help.
 Chee Wee Koh posted on Wednesday, February 24, 2016 - 6:26 pm
Hi!

I just read the post above between Anna and Tihomir after posting a very similar question elsewhere in this forum (sorry!). Like to check if Timohir's response applies to my case, because I am running LPA instead of LCA.

I have a latent profile variable based on 2 continuous indicator variables (restriction on local independence is relaxed). In addition, I am examining gender (M/F) as a covariate and a few distal outcomes. I also followed Kankaras et al. (2010) and found that I need to specific a direct effect from gender to one of indicators (u1). I am more interested in the relationships between profile and distal outcomes rather than gender differences in latent profile membership. Can I use manual BCH and correct for the 'DIF' using the following in step 1?

MODEL:
%overall%
u1 on gender;

Thank you!
 Tihomir Asparouhov posted on Thursday, February 25, 2016 - 2:57 pm
You can use either the manual or the automatic procedure. The manual procedure should be used to accommodate more complicated models involving the latent profile and the distal outcomes (such as regression of a distal outcome on the latent profile and another covariate). If you are only interested in the effect of the latent profile on the distal outcomes you should use the automatic procedure, i.e., all you need to do is to add in the variable command "auxiliary=distal outcome (bch);"

The 'DIF' issue should not affect your decision on manual v.s. automatic BCH, and the 'DIF' modeling can be accommodated in both the manual and the automatic BCH.
 Chee Wee Koh posted on Thursday, February 25, 2016 - 3:21 pm
Dear Timohir,

Thank you very much! One more question. My data shows that gender is also a covariate of my distal outcome. Therefore apart from specifying the non-MI involving gender in step 1, I also intend to regress the outcome on gender (and latent profile) in step 2 using manual BCH. Is this ok?
 Tihomir Asparouhov posted on Friday, February 26, 2016 - 12:10 pm
Yes