Estimating indirect effects
Message/Author
 Anonymous posted on Tuesday, January 08, 2013 - 7:20 am
I have set up the following mediation model in Mplus using WLSMV, where Y is a dichotomous outcome variable, M is a continuous mediating variable, and age and age2 are centered continuous predictors:

Y on age (p1);
Y on age2(p2);
Y on M (p3);
M on age (p4);
M on age2 (p5);
[Y] (i1);
[M] (i2);

I can estimate the direct probability of Y for any given age using the model constraint command with phi(i1-(p1*age)-(p2*age2)).

Can I estimate the indirect probability of Y for any given age similarly? I would like to construct a plot of the proportion indirect effect/total effect as a function of age, or something analogous.

Thank you
 Bengt O. Muthen posted on Tuesday, January 08, 2013 - 3:02 pm
See the recent discussion thread with Todd Hartman starting January 5.
 Anonymous posted on Thursday, January 31, 2013 - 7:13 am
This is an extremely helpful paper! I have one question regarding the case of a binary outcome and continuous mediator:

In the Mplus code, Table 32, Page 118, I was expecting the dir line to be something of the form

dir=beta3*gamma0+beta2+beta3*gamma2*c

where c is agg1, which has been standardized.

However dir is given as

dir=beta3*gamma0+beta2.

Could you explain why this is please?
Is this because the direct effects would need to be estimated for different specified values of c=agg1, and hence everything has been calculated conditional for the mean value for agg?
 Bengt O. Muthen posted on Thursday, January 31, 2013 - 9:05 am
Your dir formula is correct; that's the general form. In Table 32 the direct effect is evaluated at the average of c (agg1) which is zero in this case so the last term falls out.
 Anonymous posted on Monday, February 04, 2013 - 4:46 am
Thank you. I have now fitted my model: there are two exogenous predictors X and Xsquared (continuous), a continuous mediating variable M and a dichomotous outcome Y. The effect associated with M is allowed to vary with X (p<0.001). Using the results from the paper I am now able to estimate parameters for:

direct effect associated with X on Y (a)
direct effect associated with Xsq on Y (b)
indirect effect of X on Y (c)
indirect effect of Xsq on Y (d).

I'd like to convert these results onto a probability scale as they are not very interpretable as they stand. In the paper you show how this can be done when the exogenous variable is binary (treatment/no treatment) and there is only one term. I have 2 continuous terms. Can this be extended easily to the above example?

Is it correct to estimate for each value of X the total probability of Y as

phi([Y$1]-((a+c)*x))-((b+d)*xsquared))) and the direct probability as phi([Y$1]-(a*x)-(c*xsquared))?
 Bengt O. Muthen posted on Monday, February 04, 2013 - 5:42 pm
Page 16 of my paper shows how to express the effects on a binary outcome in the probability scale.

When X is a continuous instead of a binary variable, the formulas are modified in line with VanderWeele and Vansteelandt (2009, Appendix). The direct and indirect effects are

DE=(\beta_2+\beta_3 \gamma_0)) \; (x-x'),
TIE = (\beta_1 \gamma_1+\beta_3 \gamma_1 x) (x-x').

For example, x' may represent the mean of X and x may represent one standard deviation above the mean. If X is standardized this results in the same formulas as for a 0/1 X variable. If X is centered, x'=0 and x is the standard deviation of X.
 Anonymous posted on Wednesday, February 13, 2013 - 8:38 am
Is it possible in Mplus to have a count variable as a mediator which is given a zero-inflated Poisson distribution?
 Bengt O. Muthen posted on Wednesday, February 13, 2013 - 2:33 pm
I don't know how that would be done. In the m->y relationship it isn't clear how m should be treated. The indirect effect is also unclear.