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 Tor Neilands posted on Tuesday, April 09, 2013 - 11:57 am
I have fitted the following model using Mplus 7:

Type = complex ;
Param = Theta ;

Peers BY friendci friendot ;
Exposure BY iad2 mad2 sad2 tvmoviea ;

Peers promoite ON Exposure familyto
sex grade Nonwhite ;
ctobacco ON Exposure Peers promoite
familyto sex grade Nonwhite ;

familyto ;
grade ;
Nonwhite ;
sex ;

Peers with promoite ;

Model Indirect:
ctobacco IND Exposure ;

This model examines the association of a latent tobacco advertising variable (measured by four ordinal indicators: internet ad exposure, magazine ad exposure, store ad exposure, TV/movies ad exposure) with current tobacco use, a binary variable, mediated by an ordinal variable, willingness to use tobacco promotional products (promoite) and a continuous latent variable (peers).

The model fits the data well. Several collaborators are now curious to learn what the specific effect of tobacco ad exposure in TV and movies is on the current tobacco use outcome. E.g., they would like to compare what the model-implied probability is for respondents with a '5' (maximum self-reported exposure) to those with a '1' (minimum self-reported exposure). Is there a way to address that type of question using Mplus?
 Bengt O. Muthen posted on Tuesday, April 09, 2013 - 1:53 pm
You can do that. Because you have a binary distal outcome you want to follow the ideas of

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.
 Tor Neilands posted on Tuesday, April 09, 2013 - 9:27 pm
Thank you, Bengt. I've read the excellent paper to which you refer here (sidebar suggestion: anything you and the Mplus team can do to build in features in future Mplus versions to make causal mediation of this type more easily available in Mplus, e.g., something similar to the current MODEL INDIRECT statement, would be greeted very enthusiastically in the public health community. I don't know if it's statistically feasible to build in such a feature, but if it is, it would be a boon to public health researchers).

A follow-up question about my example model, if I may: All of the examples I recall from the 2011 paper have exogenous predictors. My observed TV/Movie ad exposure variable is endogenous because it's one of four indicators of the latent ad exposure variable. I will re-read the 2011 paper, but any guidance on how to adapt the most relevant example (6.6 + appendix example 14.4, I'm assuming) given my endogenous indicator would be greatly appreciated.
 Tor Neilands posted on Wednesday, April 10, 2013 - 8:36 am
I realize my previous message may have been unclear. My initial thought was to change the scaling units of the latent tobacco exposure variable "exposure" by overriding the Mplus default of fixing the first indicator's factor loading to 1 by freeing the factor loading for iad2 and fixing the factor loading for tvmoviea to 1. That would put the units of the exposure latent variable in tvmoviea units (tvmoviea is the variable for which we want to obtain model-implied probablities when tvmoviea = 1 and tvmoviea = 5).

But I'm guessing that's not sufficient because if I then use exposure as the upstream predictor in the causal mediation syntax shown in the 2011 paper, the probabilities estimated would be based on the shared variance among all four predictors, not just tvmoviea. I think what I need is the model-based probabilities at tvmoviea = 1 and tvmoviea = 5, not exposure = 1 and exposure = 5, if that makes sense? And where I'm stuck is how to build that into the causal mediation examples you have in the 2011 paper. Thanks again for any suggestions you can offer.
 Tor Neilands posted on Wednesday, April 10, 2013 - 8:59 am
I see that I wrote "...all four predictors..." when I meant to write "...all four indicators...". My apologies for any confusion that may have caused.

I thought of another way of expressing what I'm looking for: I need an expression for the portion of variance in the latent exposure variable attributable to the observed variable tvmoviea (I assume that expression would be some combination of the factor loading for the tvmoviea variable and its item thresholds?). I would then plug that expression into the causal mediation examples (modified accordingly) shown in the 2011 paper to obtain the probabilities for the distal binary outcome ctobacco when tvmoviea (purged of measurement error) = 1 and when it = 5.

My apologies for so many posts on this topic!
 Bengt O. Muthen posted on Wednesday, April 10, 2013 - 12:04 pm
Tricky situation. I wonder if it is satisfactory to your clients if you simplify the situation a bit by focusing on standard deviation changes in the exposure factor. As part of the exposure factor model, you can express what the expected change in your tvmovie indicator is as a function of changes in the exposure factor. If you set the factor metric to mean/variance 0/1, you get

E(y | f=0) = nu (intercept of tvmovie),
E(y | f=1) = nu + lambda*1 (1 SD above the factor mean)


You can then see for which exposure factor change you would get the tvmovie indicator change the clients are interested in. So an indirect approach. The SD change in the factor can then be used in the indirect effects.

It seems like you should stick to your factor given that you formulated a factor model. Otherwise, use just the tvmovie indicator as the only, observed exposure representative.
 Bengt O. Muthen posted on Wednesday, April 10, 2013 - 12:05 pm
And, yes, in a future version we hope to simplify/automate getting the effects using the causal formulas from the paper.
 Tor Neilands posted on Wednesday, April 10, 2013 - 2:38 pm
Thank you, Bengt, this is great news about the future version automating causal effects.

I also appreciate your suggested approach involving SD change. I'll give that a try. One clarifying question: the tvmovie indicator is ordinal with five levels ranging from 1-5. So, there are four thresholds rather than one intercept. How would the formula you presented above work in the ordinal indicator context? (or should I switch tvmovie to be continuous?)

Yes, I would like to stick with the factor model if possible because if I change tvmovie to be a separate independent variable with exposure measured by the three remaining indicators, a suppression-type effect occurs, with what was a significant positive effect of ad exposure becoming significantly negative, which is contrary to substantive expectations and what is known from the literature in this area.

As you noted, of course, it is possible to do away with the latent exposure variable entirely and the other three measurements completely and just use tvmovie as the sole exposure variable. I'll reserve that as a backup plan.

Thanks again.
 Bengt O. Muthen posted on Thursday, April 11, 2013 - 8:38 am
Unless the tvmovie indicator has strong floor or ceiling effects, I would treat it as continuous.
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