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st: New on SSC: -khb- for decomposing total effects into direct/indirect effects

From   Ulrich Kohler <>
To   statalist <>
Subject   st: New on SSC: -khb- for decomposing total effects into direct/indirect effects
Date   Wed, 22 Dec 2010 11:27:32 +0100

Hello Statalisters,

Courtesy of Kit Baum, the new Stata ado -khb- can be downloaded from SSC

. ssc install khb

-khb- decomposes the total effect of a variable into direct and indirect
effects using the (brand new) KHB-method developed by Karlson, Holm, and
Breen (2010). The method is developed for binary and logit and probit
models, but this command also implements the method for other nonlinear
probability models (ordered and multinomial) and linear regression.
Contrary to other decomposition methods, the KHB-method gives unbiased
decompositions, decomposes effects of both discrete and continuous
variables, and provides analytically derived statistical tests for many
models of the GLM family.

In linear regression models, decomposing the total effect into direct
and indirect effects is straightforward. The decomposition is done by
comparing the estimated coefficient of a key variable of interest
between a "reduced model" without a hypothesized mediator variable and a
"full model" which include this mediator. The difference between the
estimated coefficient of the key-variable of the two models expresses
the "indirect effect", i.e., the part of the total effect running
through the mediating variable.

The strategy described for linear models cannot be used in the context
of nonlinear probability models such as logit and probit, because the
estimated coefficients of these models are not comparable between
different models. The reason is a rescaling of the model induced by the
joint identification of the coefficients and error variances. The
KHB-method solves this problem. It allows the decomposition of total
effects into direct and indirect effects for many models of the GLM
framework, including logit, probit, ologit, oprobit, and mlogit. 

The basic idea of the KHB-method is to compare the full model with a
reduced model that substitutes the mediators by the residuals of the
mediators from a regression of the mediators on the key-variables of
interest (see Karlson/Holm/Breen 2010 for details). 


Karlson, K.B./Holm, A./Breen, R. (2010): Comparing Regression
Coefficients Between Models using Logit and Probit. A New Method. (Under

Karlson, K.B./Holm, A. (Accepted for publication): Decomposing primary
and secondary effects: A new decomposition method. Research in
Stratification and Social Mobility.

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