Categorical predictor in causal media...
Message/Author
 Alejandro Sevilla posted on Monday, January 25, 2016 - 3:55 pm
The predictor of my model is
parents' educational levels. I have been using Hayes and Preacher (2014) suggestion
to derive indirect, direct and total effects for each of the 3 dummy
variables created from the 4-category predictor. All the effects are
interpreted relative to the reference category (pared_1).
y IND pared_2;
y IND pared_3;
y IND pared_4;

However, I am not completely sure if in causal mediation the TNIEs and PNDEs
derived from every dummy variable of parents' education can also be
interpreted relative to the reference category of parents' education.

y IND gpa pared_2;
y IND gpa pared_3;
y IND gpa pared_4;

y is binary and the mediator (gpa) is continuous

Or the TNIEs and PNDEs are actually comparing the dummy variable analysed
against all other categories from the whole sample. For instance, pared_2=1
vs pared_2=0 which actually will mean comparing against all other
individuals in the sample that have parents with other levels of education
rather than 'pared_2' and not only the reference category?

My model is
y ON gpa
pared_2
pared_3
pared_4;
gpa ON pared_2
pared_3
pared_4;
 Bengt O. Muthen posted on Monday, January 25, 2016 - 6:16 pm
If you say

y IND gpa pared_2;

with a binary y you get the new counterfactually-defined causal effects. In this case, the other pared dummies will be viewed as "control" variables and the effects are conditioned on them being zero.
 Alejandro Sevilla posted on Wednesday, January 27, 2016 - 8:31 am
Thank you Prof. Muthen.
I was wondering if there is a way to get the counterfactually-defined causal effects only related to the reference category for every category of parental education.
 Bengt O. Muthen posted on Wednesday, January 27, 2016 - 3:20 pm
Won't zero on control variables give you that? For a particular dummy variable, seen as the exposure variable, being 1 instead of 0, won't the other dummy variables be zero?
 Alejandro Sevilla posted on Wednesday, January 27, 2016 - 4:10 pm
Yes, the other dummies are zero. So, deriving the effects for every dummy variable will mean having the relative effects to the reference category?

This is what I have, deriving the effects manually (following Muthen, 2011)

MODEL:
tr_pse ON gpa (b)
pared_2 (cp1)
pared_3 (cp2)
pared_4 (cp3);
[tr_pse\$1] (tres);
gpa ON pared_2 (a1)
pared_3 (a2)
pared_4 (a3);
[gpa] (a0);
gpa (sig2);
 Alejandro Sevilla posted on Wednesday, January 27, 2016 - 4:11 pm
MODEL CONSTRAINT:
NEW (arg11_1 arg11_2 arg11_3 arg10_1 arg10_2 arg10_3 arg00 v1 v0 prob11_1 prob11_2 prob11_3 prob10_1 prob10_2 prob10_3 prob00 indir1 indir2 indir3 direct1 direct2 direct3);
arg11_1= -tres+cp1+b*(a0+a1);
arg11_2= -tres+cp2+b*(a0+a2);
arg11_3= -tres+cp3+b*(a0+a3);
arg10_1= -tres+cp1+b*a0;
arg10_2= -tres+cp2+b*a0;
arg10_3= -tres+cp3+b*a0;
arg00= -tres+b*a0;
v= b^2*sig2+1;
prob11_1= arg11_1/sqrt(v);
prob11_2= arg11_2/sqrt(v);
prob11_3= arg11_3/sqrt(v);
prob10_1= arg10_1/sqrt(v);
prob10_2= arg10_2/sqrt(v);
prob10_3= arg10_3/sqrt(v);
prob00= arg00/sqrt(v);
indir1= phi(prob11_1)-phi(prob10_1);
indir2= phi(prob11_2)-phi(prob10_2);
indir3= phi(prob11_3)-phi(prob10_3);
direct1= phi(prob10_1)-phi(prob00);
direct2= phi(prob10_2)-phi(prob00);
direct3= phi(prob10_3)-phi(prob00);
 Alejandro Sevilla posted on Monday, February 01, 2016 - 8:53 am
I found that 'medflex' (an R-package) explicitly takes into account multicategorical exposure variables in a causal mediation setting. Comparing indirect and direct effects derived from the same model above using medflex (without covariates or interaction between in the exposure and the mediator) gives me almost identical results are those derived in Mplus as z-scores (i.e. indir1= prob11_1-prob10_1, etc.).

I was thinking that I am finding the same results because I am actually comparing the dummy variable of interest including the constant/intercept which accounts for the effect of the reference category and setting aside the effect of the coefficients from the other dummies (not included in 'arg' variables). Therefore, Hayes and Preacher (2014) interpretation in the standard mediation modelling is also applicable in causal mediation in Mplus.

Is that the case?
 Bengt O. Muthen posted on Monday, February 01, 2016 - 6:17 pm
I think this is the case.
 Alejandro Sevilla posted on Tuesday, February 02, 2016 - 1:43 am
Thank you!
 Alejandro Sevilla posted on Friday, February 26, 2016 - 10:37 am
Prof Muthen

I was wondering whether in causal mediation having covariates as dummy variables might have an effect on the derivation/interpretation of causally-defined effects.
For instance, adding the dummy variables of male and smoker as covariates to a mediation model will make that the constant and intercept terms now will be accounting for the effects of female and non-smoker alongside to the control group.
 Bengt O. Muthen posted on Friday, February 26, 2016 - 11:11 am
In conventional models (linear models for continuous DVs, no X, M interaction) the control variables (covariates) do not play a role in the indirect or direct effects. But in other cases they do and would be interpreted as you say.
 Alejandro Sevilla posted on Friday, February 26, 2016 - 12:02 pm
Thanks. What would be the case for a continuous mediator, binary outcome but no interaction (X*M)?
 Bengt O. Muthen posted on Friday, February 26, 2016 - 2:34 pm
They play a role there. See my 2011 paper.