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st: Direct and indirect effects for logit models

From   Cameron McIntosh <>
Subject   st: Direct and indirect effects for logit models
Date   Sat, 22 Aug 2009 14:49:40 -0400

Hi Fardad,

The best approach, in my opinion, would be SEM. -gllamm- can easily handle non-linear path models, and should be pretty fast if you have no latent variables:

However, please be aware that that testing mediation/indirect effects in the non-linear case is not nearly as straightforward as in the linear case. Make sure you read up on this literature and familiarize yourself with the issues before proceeding:

MacKinnon, D.P., Lockwood, C.M., Brown, C.H., Wang, W., & Hoffman, J.M. (2007). The intermediate endpoint effect in logistic and probit regression. Clinical Trials, 4(5), 499-513.

Li, Y., Schneider, J.A., & Bennett, D.A. (2007). Estimation of the mediation effect with a binary mediator. Statistics in Medicine,  26(18), 3398-3414.

Eshima, N., Tabata, M., & Zhi, G. (2001). Path analysis with logistic regression models: effect analysis of fully recursive causal systems of categorical variables. Journal of the Japanese Statistical Society, 31(1), 1-14.

MacKinnon, D.P. (2008). Introduction to statistical mediation analysis. Mahwah, NJ: Erlbaum.

Schluchter, M.D. (2008). Flexible approaches to computing mediated effects in generalized linear models: generalized estimating equations
and bootstrapping. Multivariate Behavioral Research, 43(2), 268-288.


> Date: Sat, 22 Aug 2009 17:42:13 +0200
> Subject: st: Direct and indirect effects for logit models
> From:
> To:
> Dear Lister,
> I'm doing a research to distinguish and compare the direct and
> indirect effects of enterprise systems (such as erp, scm, crm, etc.)
> on firm performance using a firm-level dataset. I'm using conditional
> logit (clogit) to control for market-specific fixed-effects in my
> sample; you can think of a market as sector X in country Y. This is
> seemingly a preferred approach than adding (a lot of) separate sector
> and country dummies into the model; the method is described by
> Chamberlain (1980).
> Now the main issue is indeed to rigorously separate the direct and
> indirect effects of enterprise systems adoption on firm performance.
> Performance is measured as a dummy variable indicating if the firm has
> been profitable or not or alternatively if it has experienced revenue
> growth or not. The enterprise systems adoption is measured through
> separate dummy variables for different applications such ERP, SCM,
> CRM, etc. indicating if the firm uses a specific application or not.
> For comparative purposes, these adoption variables shall be considered
> simultaneously in the model.
> In addition to the direct effect of these systems on firm performance,
> their impact is also mediated through product and process innovation,
> which are measured as separate dummies indicating if the firm has had
> product and/or process innovation. So, ignoring the coefficients and
> error terms, for simplicity, the available equations can be shown as:
> 1- ln(odds(performance)) = erp + scm + crm + control
> 2- ln(odds(product_innov)) = erp + scm + crm + control
> 3- ln(odds(process_innov)) = erp + scm + crm + control
> The “control” is a vector of control variables including several dummy
> and continuous variables to control for size, IT maturity, etc.
> At this stage, I started to look into the literature (and there is
> plenty of them in different fields :-((() and found several references
> to implement my model specification in STATA; I’m really confused
> which method is relevant/applicable and which not:
> A. As a simple approach, I can run model (1) and separately another
> model which has extra innovation variables as explanatory variables
> (i.e. ln(odds(performance)) = product_innov + process_innov + erp +
> scm + crm + control) to compare the direct and indirect effects. If
> I’m right, the difference between the estimated coefficients of
> interest (i.e. erp, scm and crm) between the two models indicates the
> indirect effect.
> B. I can use SEM to simultaneously estimate the set of three Eq. (1),
> (2) and (3); however, I don't know exactly how I can do SEM for
> non-linear models in STATA and further how the direct and indirect
> effects should be calculated afterwards.
> C. I can use a pseudo-2SLS method, in which I first run (2) and (3)
> and then insert the predicted values of product and process innovation
> as extra explanatory variables into (1); this is similar to approach
> A, except that predicted values of innovation variables are used
> rather than their actual 0/1 values. I still don’t know if the
> prediction procedure indeed generates valid predicts in the range
> [0,1].
> D. As an alternative of method C, I can add an additional regressor to
> (2) and (3) when predicting innovation outcomes. The percentage of
> highly-educated employees can serve as a good instrument here. This
> way, the set of control variables includes this additional variable in
> (2) and (3) but not in (1).
> E. I can use the IVE-GMM method for log-linear models; I know it
> exists in STATA 11 but honestly don't know how to use it or if it
> serves my objectives. I’m also not aware of any additional assumptions
> required for this method.
> F. I can use the -ldecomp command in STATA but seemingly it doesn't
> allow for multiple direct variables to be considered. For me it is
> important to have erp, scm and crm at the same time in the model to
> compare their relative impacts on the performance outcome.
> G. There is also the -fairlie method; I'm not familiar with it and
> also don't know exactly how it differs from -ldecomp or similar
> commands.
> All in all, I'm really puzzled :-(( don't know what method(s) are the
> favorable ones in terms of practical interpretations, consistency of
> results and estimation efficiency.
> I thought, you might be able to provide me with any guideline, advice
> or recommendation, concerning your expertise and experience, as I'm
> not an econometrician per se.
> I know this is a very long email and would take a lot of your time to
> read and perhaps reflect on; however, I should have explained what
> happened to me within the past weeks. Nevertheless, I really
> appreciate your help and support.
> Many thanks indeed,
> Fardad
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