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 Stephan Junker posted on Wednesday, January 31, 2018 - 4:34 pm
Dear all,
let's say I have the following model.

Y on M X
M on X

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,

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
 Stephan Junker posted on Thursday, February 01, 2018 - 5:52 am
I forgot to menation. I'am doing a Multiple Group analysis (two groups) and included covariates.

So it is actually

Y on X1 X2 M
M on X1 X2

M is an ordered categorical Mediator with three categories
X1 is a dummy variable


I am interested in the comparisson of the Y value considering the total effect of X1 if X1 is zero and if X1 is one in both groups
 Bengt O. Muthen posted on Thursday, February 01, 2018 - 2:26 pm
The Hayes-Preacher article talks about a multicategory X, not a multicategory M. You have a binary X and multicategory M. The total effect is the mean of Y for X=1 minus the mean of Y for X=0.

In your second message I don't know if you imply that X2 represents group membership.

Indirect effects with an ordinal M is discussed in Chapter 8 of our book Regression and Mediation Analysis using Mplus.
 Stephan Junker posted on Friday, February 02, 2018 - 1:03 am
Thank you very much for your answer. Let me rephrase my question.
My question is how to calculate the unadjusted mean Hayes and Preacher talk about when M is categorical.

My understanding is that I would need the intercept of M* for this. However I dont know how to calculate this when M has more then two categories.

X2 is just a control variable.

I tried to get our library to get this book since almost a year however they say their supplier says it's out of stock.
 Bengt O. Muthen posted on Friday, February 02, 2018 - 3:16 pm
Which page of Hayes and Preacher do they talk about the unadjusted mean when M is categorical?
 Stephan Junker posted on Saturday, February 03, 2018 - 12:42 am
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.

Thanks again
 Stephan Junker posted on Saturday, February 03, 2018 - 2:23 am
Dear Dr. Muthén,
I think I found the answer I was lookig for.
As the notation in stata and MPlus seems to be the same - concerning ordered probit regression - the constant/intercept of M* is a=-t$1, right?

So the value of Y considering the total effect of X=0 on Y would be:

E(Y |X=0 & M*=0)=Y_i=Intercept of Y on X M
a=effect of X->M*
b=effect of M*->Y
c'=effect of X->Y

E(Y|X=0)=unadjusted mean of "control"

E(Y|X=0)=b*-t$1+Y_i=unadjusted mean of control="total effect intercept"

"unadjusted mean of control"+"total effect of X=1"=unadjusted mean of X=1

Best regards,
 Bengt O. Muthen posted on Saturday, February 03, 2018 - 2:27 pm
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.
 Stephan Junker posted on Sunday, February 04, 2018 - 1:29 am
The unajusted mean in the Hayes an Preacher Paper is on page 460 the third section. They talk about the unajusted group mean on page 458 very quickly.

What I am interested in is "i3".

To explain why I am interested in it consider the following example:

2 groups: germany, england

(0=female, 1=male)
(0=highschool, 1=Bachelor, 2=Master)

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?
 Bengt O. Muthen posted on Monday, February 05, 2018 - 9:23 am
i3 is the intercept of Y as seen in Table 3. M is not involved in the third (bottom) section of that table.
 Stephan Junker posted on Tuesday, February 06, 2018 - 1:27 am
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.

You can find the MPlus Output of the Hayes and Preacher article in their appendix here:

But I think you answered my question as the intercept of M* is zero. Is this also true in multiple group analysis? The mean of M* is zero in both groups, just the values of thresholds can change?

Thanks for your patience!
 Bengt O. Muthen posted on Tuesday, February 06, 2018 - 3:43 pm
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.
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