Message/Author 

gibbon lab posted on Wednesday, October 30, 2013  2:23 pm



Dear Professors I ran a mediation model like the following: x(continuous)>y(binary)>z(continuous). 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. 


Your understanding is correct. If you don't want y* to be the predictor, you should consider the causallydefined effects in my 2011 mediation paper which you find under Papers, Mediational Modeling. 

gibbon lab posted on Tuesday, November 05, 2013  10:53 am



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(zy*>tau)E(zy*<tau) to estimate E(zy=1)E(zy=0) where tau is the threshold estimated in Mplus to dichotomize y* into y. Thanks a lot. 


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  8:14 am



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. 


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. 


The expectation looks correct for WLSMV. 

gibbon lab posted on Thursday, November 07, 2013  10:13 am



Dear Linda, Thanks a lot. 

gibbon lab posted on Wednesday, November 13, 2013  8:00 am



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. 


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  12:13 pm



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

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