Estimating indirect effects PreviousNext
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 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


where c is agg1, which has been standardized.

However dir is given as


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


and the direct probability as

 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.
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