Model indirect with Bayes
Message/Author
 Dmitriy Poznyak posted on Wednesday, October 26, 2011 - 7:38 am
Dear Linda and Bengt,

I estimate a two-level model with mediation relationship on the macro-level. I use Bayesian estimator. It looks like the "Model indirect" statement is not available in this case. Therefore, I wonder:

1. As far as Bayesian analysis is concerned, would it be appropriate to calculate the indirect effects in a usual way by multiplying the path coefficients.

2. If yes, how can I estimate whether the coefficients for the indirect effects are significant? Can I use Delta parameterization to derive the coefficients, as Bollen describes in the book or would it be something else here?

Thank you,
Dmitriy
 Dmitriy Poznyak posted on Wednesday, October 26, 2011 - 9:32 am
A quick follow-up on my own post: can I manually calculate standard errors of the estimates when using Bayesian approach? If this were the case, then I could (supposedly) calculate Sobel's test.
 Linda K. Muthen posted on Wednesday, October 26, 2011 - 1:22 pm
What are the scales of your mediator and final outcome?
 Dmitriy Poznyak posted on Thursday, October 27, 2011 - 2:15 am
Dear Linda,

To clarify first, I test mediation effects only on the between-level.

My exogenous variables are continuous.

My mediators are the variables that function on both within- and between-levels. They are modeled as categorical on the within-level (whether respondent considers a problem as nationally important; yes/no), but on the macro-level they become continuous variables (proportion of the respondents in a given year who named a certain problem nationally important). Therefore, the mediators on the between-level are also continuous.

My final outcome is a latent variable on the between level, which is modeled by four categorical indicators.
 Bengt O. Muthen posted on Thursday, October 27, 2011 - 8:56 am
Because all of your variables are continuous (on Between), you can use the product formula for the indirect effect. You handle this via Model Constraint where you express the effect as a New parameter using labels for the Model parameters involved. The SEs are automatically computed by Mplus using the Delta method that Sobel used.
 Bengt O. Muthen posted on Thursday, October 27, 2011 - 10:06 am
I just remembered that you said you wanted to use Bayes. In this case the SEs are not computed via the Delta method but the New parameter with the indirect effect gets a posterior distribution where you can read off the 95% interval - that also takes into account any non-normality of the indirect effect estimate distribution.
 Dmitriy Poznyak posted on Thursday, October 27, 2011 - 11:27 am
Dear Bengt,

Thank you, this helped. I did use "model constraint" statement and got the necessary estimates. I was wondering though - there is no STDYX output for the indirect effects. Of course, I can compute the standardized values manually, but I am curious why Mplus won't give them by default?
 Bengt O. Muthen posted on Friday, October 28, 2011 - 9:56 am
I think you are asking wy we don't have Model Indirect yet for Twolevel - no particular reason except many other things to implement. For a New parameter in Model Constraint that you create as an indirect effect product you get STDYX there.
 Dmitriy Poznyak posted on Friday, October 28, 2011 - 11:30 am
Not really. In my case I only get the unstandardized effects for the new parameters. This is what surprised me. This is not much relevant however, since I can calculate the standardized coefficients manually.
 Bengt O. Muthen posted on Friday, October 28, 2011 - 4:09 pm
So you were asking why we don't standardize New parameters in Model Constraint? That would require another level of sophistication where we would need to go back to the Model statements to keep track of what model parameter ingredients the new parameter uses and which observed and latent variables these parameters connect with, in order to standardize the New parameter correctly.
 Johan Ng posted on Wednesday, June 13, 2012 - 2:21 pm
Dear Bengt & Linda

To continue with the above discussion, although one can manually calculate the standardized point estimates for the indirect effects, but is there a way to do so for the credibility intervals?

Would standardizing the inputs do the trick?

Many thanks!
 Bengt O. Muthen posted on Wednesday, June 13, 2012 - 5:31 pm
You can get CIs for the standardized estimates that you define in Model Constraint because Model Constraint also gives you SEs.
 Johan Ng posted on Thursday, June 14, 2012 - 12:51 am
Dear Bengt

Thanks for your swift response (as always!). Apologies for omitting a piece of important info in my previous question - I was using the BAYES estimator. Sorry for not making that clear previously.

So the phrase my question again: When using the BAYES estimator, together with Model Constraint, is there a way to get standardized credibility intervals?

Thanks again!
 Bengt O. Muthen posted on Thursday, June 14, 2012 - 3:51 pm
If you use Bayes you always get CIs, also for parameters that you define in Model Constraint, including parameters that you define as standardized. It's a good way to take care of non-normal distributions for indirect effects, for instance.
 MT posted on Monday, August 27, 2012 - 1:58 am
Dear Linda and Bengt,

I also estimate a twolevel model with mediators using Bayes estimation. In this model, I would like to test the indirect effect of X on Y via M1 and M2. Can this be computed by simply using model constraint:
indirect = a*b*c?

Thank you very much!
 Linda K. Muthen posted on Tuesday, August 28, 2012 - 11:12 am

x -> m1 -> m2 -> y

this is correct in some cases.

See the following paper on the website for details:

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.
 Anika Fäsche Heinz posted on Thursday, March 06, 2014 - 6:15 am
Dear Mplus team,

I'm running a twolevel path model using Bayes estimation. I have multiple parallel mediators on the within level and the mediations are also only modeled on the within level.

However, when I specify the indirect effect via the usual MODEL CONSTRAINT command, the new parameters for the indirect effects appear in the between level and not in the within level section of the output. What does that mean? On which level are they modeled then?