gibbon lab posted on Wednesday, October 30, 2013 - 2:23 pm
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.
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 - 10:53 am
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.
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
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.