

Marginal effects of indirect coeffici... 

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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 unstandardized coefficients. Unstandardized direct coefficients: 1. X > Y: 0.4 2. X > B: 0.3 3. B > Y: 0.2 Unstandardized 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 unstandardized coefficient by the ratio # of noncensored 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 


Do you have a reference for the following: "multiply unstandardized coefficient by the ratio # of noncensored observations to # of all observations" 


Yes. I referenced following contents. Greene, W. H, 2008, Econometric Analysis,p.872 Is it wrong? or Is my understanding wrong? 


Will get back to you about this. 


For the censored variable I think the marginal effect that you refer to is the derivative of E(yx) 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 reducedform 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 causallyderived 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. 

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