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

["Ariel Linden, DrPH" <ariel.linden@gmail.com>]

Hi Adam,

I won't get long winded here, but when you have categorical mediators and/or
outcomes, you need to standardize the given variables in order to get them
(Y and M) on the same scale. There are several references I could point you
to, but I would start by reading the references below, and more importantly,
consider using the user-written command -khb- (findit khb), which these
references refer to. 

Kohler, U., Karlson, K.B., Holm A.: Comparing coefficients of nested
nonlinear probability models. The Stata Journal 11, 420-438 (2011)

Karlson,  K.B., Holm, A.: Decomposing primary and secondary effects: A new
decomposition method. Research in Stratification and Social Mobility 29,
221-237 (2011)

Karlson, K.B., Holm, A., Breen. R.: Comparing regression coefficients
between models using logit and probit: A new method. Sociological
Methodology 42, XX (2012) 

Ariel

Date: Wed, 11 Jul 2012 15:30:23 +0800 (SGT)
From: Adam Cheung <adam_kalok@yahoo.com.hk>
Subject: st: Standardization necessary for mediation analysis with binary
outcome? About binary_mediation ado

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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