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?
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.