Marginal effects of indirect coeffici...
Message/Author
 Seung-Nam Kim posted on Tuesday, October 11, 2011 - 9:51 pm
I have some questions about computing marginal effect of indirect coefficient consist of categorical variable and censored variable.

My conceptual model is as follows.

Y on B X
B on X

X is continuous exogenous variable.
B is binary endogenous variable.
Y is censored endogenous variable.

There are 4 different un-standardized coefficients.

Un-standardized direct coefficients:
1. X -> Y: 0.4
2. X -> B: 0.3
3. B -> Y: 0.2

Un-standardized indirect coefficients:
4. X -> B -> Y: 0.3*0.2=0.06

I`d like to compute marginal effects of all coefficients.

The first question:

Generally, when we compute marginal effect of censored regression (e, g., X->Y), we multiply un-standardized coefficient by the ratio # of non-censored observations to # of all observations.
Is this method correct to interpret the coefficient from Mplus.

The second question:
How about the coefficient, X -> B. In this case, do we have to use general method or other ways?

The last question:
If we can use general method (computing marginal effect), can we use the marginal effect of the indirect coefficient by multiplying two marginal effects each other?

Thanks. I am looking forward your respond.

Seungnam
 Linda K. Muthen posted on Wednesday, October 12, 2011 - 12:12 pm
Do you have a reference for the following:

"multiply un-standardized coefficient by the ratio # of non-censored observations to # of all observations"
 Seung-Nam Kim posted on Thursday, October 13, 2011 - 2:40 am
Yes. I referenced following contents.

Greene, W. H, 2008, Econometric Analysis,p.872

Is it wrong? or Is my understanding wrong?
 Bengt O. Muthen posted on Thursday, October 13, 2011 - 9:10 pm
 Bengt O. Muthen posted on Saturday, October 15, 2011 - 5:17 pm
For the censored variable I think the marginal effect that you refer to is the derivative of E(y|x) with respect to x, which is as you say is the product of the probability of y>0 and the slope on x for the case of censoring from below at 0. Those who don't have Greene (2008) can also see this in Long (1997; p. 209) in his book on regression with categorical and limited DVs.

You are interested in the indirect effect of a variable X, say, where the mediator M is binary and the outcome Y is censored, asking if two marginal effects can be multiplied. The answer is a bit long. One way to approach this is to consider the reduced-form regression for Y on X. An indirect effect in terms of a simple product is relevant when both the M and the Y regression is linear. For your situation both are linear if instead of Y you consider the continuous latent response variable Y* and instead of M the latent mediator M*.

For simplicity, first assume that M is continuous. Then the product of the raw X slope and the raw M slope times the probability y>0 would be your marginal effect. It wouldn't be a causally-derived indirect effect, however, but that is a longer story.

Now turn to M being binary with a continuous M*. The same holds as in the above paragraph. For this analysis you need to use WLSMV which treats a binary mediator as M* in both regressions.