M is an ordered categorical Mediator with three categories X is a dummy variable
Now I want to compare the value of Y considering the total effect of X=1 to X=0.
As far as I understand that means comparing: E(Y|X=1 & E(M|X=1)) to E(Y|X=0 & E(M|X=0))
I think I understood from the paper by Hayes and Preacher (2014) how to calculate these values. However for this I would need the intercept of "M on X" because it is the value of M if X=0. As M is a categorical Mediator I only get two thresholds. So I don't know how I get the intercept of the underlying continuous M* Variable.
I would appreciate if sombody could help me with this.
Best regards, Stephan
Hayes, A. F. & Preacher, K. J. (2014). Statistical mediation analysis with a multicategorical independent variable. British Journal of Mathematical and Statistical Psychology, 67, 451–470. http://doi.org/10.1111/bmsp.12028
Sorry it seems there is a misunderstandening. Hayes and Preacher, don't talk about unadjusted means when M is categorical. Just when M is continious.
However I thought when you use the wlsmv estimator in a path model, the "underlying latent variable approach" is used when M is predicted and when M is predictor.
So when M* is the underlying variable and this is continious, my understanding is that I can proceed like in the Hayes and Preacher article, when I know about the values of M* instead of M. So this is why I am interested in getting the intercept of M* when M is categorcial with more then two categories.
Yes, WLSMV works with M*. Its intercept is zero. For a 3-category M, there are 2 thresholds for M*. With a binary M, the negative of the threshold can be seen as the intercept with a new threshold being zero. With a multicategory M there is no such correspondence.
I don't know what you refer to when you say "unadjusted mean". I see an adjusted mean expressed in equation (4) of the Hayes-Preacher paper. I also don't know why you would be interested in anything but the usual direct and indirect effects.
Now what I want to say is what income does the model predict for males and females in England and Germany taking into account, that they have different probabilities for education, which also has an influence on income.
When the intercept of M* is zero in both groups this is easy because I just need the intercept of Y, right?
They don't show how they calculated i3 but it is however not a parameter included in the output of their MPlus analysis (appendix: p2).
They specify the following Model:
M on X1 X2 Y on X1 X2 M
And get the following results:
effect of M=0.359=b intercept of Y=2.81=i_Y intercept of M=4.25=i_M
This is how they calculated i3 (they don't show):
The third equation on the bottom is to calculate the value of Y if M is not equal for all groups. This is the unadjusted mean. The mean of the control group takes into account the value of M if X1 and X2 are zero.
The second equation is the adjusted mean, M has the same value for all groups.
Table 3 says that i3 is simply obtained as the intercept in the regression of Y on the D dummies (no M).
Regarding the M* intercept of zero, you can do a more advanced model where you specify threshold invariance across the 2 groups but let the intercept be different from zero in one of the groups. It can be set up by adding a factor behind the categorical variable in line with the Mplus setup in the 2016 Wu-Eastabrook Psychometrika article on Identification in CFA with ordered variables. But I don't know that you want to go that advanced.