Re: st: Standardization necessary for mediation analysis with binary outcome? About binary_mediation ado

[William Buchanan <william@williambuchanan.net>]

Hi Adam,

I don't remember the exact paper, but you may want to look at some of the material on mediation with categorical mediators from MacKinnon and/or Muthén.  The problem with not standardizing the variable is the interpretation of the result and the theoretical framework.  With Mplus (which Preacher and Hayes have written code for), you either treats the binary mediator as a latent variable or it is standardized internally.  The big problem occurs when the computation of the indirect effect needs to be calculated because you would be computing with different metrics.

HTH,
Billy

Sent from my iPhone

On Jul 11, 2012, at 0:30, Adam Cheung <adam_kalok@yahoo.com.hk> wrote:

> Dear Statalisters, 
> 
> I am estimating an indirect effect of an independent variable X on dependent variable Y through mediator M, in which M is a continuous variable while outcome Y is a binary variable. 
> 
> I do not need to estimate the "proportion of total effect mediated". I only need a coefficient indicating the size of indirect effect for substantive interpretation (such as an unit increase in X increase how much of Y through M). 
> 
> For now, I am using "binary_mediation", written by Phil Ender, to estimate the indirect effect.  (https://www.ats.ucla.edu/stat/stata/faq/binary_mediation.htm)
> 
> In this ado, the indirect effect is "standardized".  As some have already pointed out (http://www.nrhpsych.com/mediation/logmed.html), it is not correct to compare the indirect effect with the total effect if the effects are not rescaled. 
> 
> However, since I only want to estimate the size of indirect effect. Is standardization procedure necessary in estimating the indirect effect if the outcome is binary? If I do not read wrongly, some have proposed the product of coefficients method without standardizing the the coefficients in the first place (for example, MacKinnon et al. 2007. The intermediate endpoint effect in logistic and probit regression). And in Preacher and Hayes's program for mediation analysis in other statistical packages, it seems that their programs do not standardize the coefficients before multiplying them (http://www.afhayes.com/public/sobel.pdf).  
> 
> Now, I am totally confused whether standardization is necessary in the context of mediation with dichotmous outcome with product of coefficients approach (in times that proportion of total effect mediation is not the focus). Is there any ado in Stata can do that without standardization (if it is correct to do so). I am aware that it is necessary to rescale the coefficients if we use difference in coefficients method. Since I may want a dichotmous X as well, I am worrying if standardization is problematic for any substantiive interpretation. 
> 
> 
> Thanks. 
> 
> Adam
> 
> 
> P.S. Strictly speaking, my analysis is more like an "associational" type of analysis. My data do not allow me to estimate average causal mediation effect which is to be estimated by using "medeff"(Imai et al.)
> 
> 
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