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 gibbon lab posted on Wednesday, October 30, 2013 - 7:23 pm
Dear Professors

I ran a mediation model like the following:

I used WLSMV estimation claiming that the binary mediator y is categorical. I wonder how I should interpret the coeficient, say beta2, for y(binary)->z(continuous). I understand that the model actually uses an underlying continuous variable y* in stead of y when estimating the path parameters. So if I am correct, the coefficient beta2 is the effect of y* on z (change in z when y* increases by 1 unit). But can I somehow convert this interpretation to the orginal scale of variable y? Like how much change in z when y changes from 0 to 1? Thanks a lot.
 Bengt O. Muthen posted on Thursday, October 31, 2013 - 1:34 am
Your understanding is correct.

If you don't want y* to be the predictor, you should consider the causally-defined effects in my 2011 mediation paper which you find under Papers, Mediational Modeling.
 gibbon lab posted on Tuesday, November 05, 2013 - 4:53 pm
Dear Professor,

I actually like the results from the model I ran. The interpretation for total indirect path does not bother me since x and z are both manifest variables in the model. I am trying to find a way to interpret the coefficient beta2 for the second path y(binary)->z(continuous) so that people (e.g., paper reviewers) will unstandand it.

I was just wondering if I can use E(z|y*>tau)-E(z|y*<tau) to estimate E(z|y=1)-E(z|y=0) where tau is the threshold estimated in Mplus to dichotomize y* into y. Thanks a lot.
 Linda K. Muthen posted on Tuesday, November 05, 2013 - 7:35 pm
To me y > z is z ON y. If z is continuous, the coefficient is a linear regression coefficient.
 gibbon lab posted on Wednesday, November 06, 2013 - 2:14 pm
Dear Linda,

y* is the latent continuous variable (for y) in the path analysis: x(continuous)->y(binary)->z(continuous). I understand that the coefficient beta2 for the second path is a linear regression coefficient for y* (interpreted as the change in z when y* increases by 1 unit). What does that mean for the binary variable y? What is the difference in terms of z between the two groups indicated by y? Is it still beta2? That is where I am stuck. Thanks a lot.
 Linda K. Muthen posted on Wednesday, November 06, 2013 - 5:08 pm
In the chain

x -> y -> z

where y is a binary variable, y is treated as y* using WLSMV and y using ML.

See the following paper which is available on the website for further information:

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. Submitted for publication.
 Linda K. Muthen posted on Wednesday, November 06, 2013 - 5:18 pm
The expectation looks correct for WLSMV.
 gibbon lab posted on Thursday, November 07, 2013 - 4:13 pm
Dear Linda,

Thanks a lot.
 gibbon lab posted on Wednesday, November 13, 2013 - 2:00 pm
Dear Professor,

Is it true that the marginal distribution of y* is assumed to be the standard normal distribution N(0,1) in the model? Thanks.
 Bengt O. Muthen posted on Wednesday, November 13, 2013 - 2:48 pm
Y is a binary mediator, right? In which case normality is assumed for y* conditional on x. That is, it is the residual for y* that is assumed N(0,1).
 gibbon lab posted on Wednesday, November 13, 2013 - 6:13 pm
Dear Bengt,

Yes, Y is binary. Thanks a lot for the clarification.
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