Hi Ali,

yes it is, among others with regard to

a) the nonsensical definition of mediation in terms the reduction of the association while controlling for the supposed mediator (which also concurs with confounding). Mediation is a causal concept and cannot be reduced to some magic data procedure.

b) the procedure (hierarchical regression and consideration of the increment vs. bootstrapping of the indirect effect)

c) the wrong presumptions (that there has to be an overall relationship, which is wrong).

See

Hayes, A. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76(4), 408-420.

Zhao, X., Lynch Jr, John G., Chen, Q., Lynch, J. G., Jr., & Chen, Q. (2010). Reconsidering baron and kenny: Myths and truths about mediation analysis. Journal of Consumer Research, 37(2), 197-206. doi:10.1086/651257

Kline, R. B. (2015). The mediation myth. Basic and Applied Social Psychology, 37(4), 202-213. doi:10.1080/01973533.2015.1049349

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83-104.

Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7(4), 422-445.

Pearl, J., & MacKenzie, D. (2018). The book of why. New York: Basic books.

Best,

Holger

Hi Ali,

yes it is, among others with regard to

a) the nonsensical definition of mediation in terms the reduction of the association while controlling for the supposed mediator (which also concurs with confounding). Mediation is a causal concept and cannot be reduced to some magic data procedure.

b) the procedure (hierarchical regression and consideration of the increment vs. bootstrapping of the indirect effect)

c) the wrong presumptions (that there has to be an overall relationship, which is wrong).

See

Hayes, A. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76(4), 408-420.

Zhao, X., Lynch Jr, John G., Chen, Q., Lynch, J. G., Jr., & Chen, Q. (2010). Reconsidering baron and kenny: Myths and truths about mediation analysis. Journal of Consumer Research, 37(2), 197-206. doi:10.1086/651257

Kline, R. B. (2015). The mediation myth. Basic and Applied Social Psychology, 37(4), 202-213. doi:10.1080/01973533.2015.1049349

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83-104.

Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7(4), 422-445.

Pearl, J., & MacKenzie, D. (2018). The book of why. New York: Basic books.

Best,

Holger

Dear Holger Steinmetz

What test you suggest for testing the mediation effect ?

Best ,

Alireza

We're still using CTT, so, no.

Hope this helps

Matt

Hi Alireza shabani shojaei ,

a better alternative (see the Hayes paper) is to focus on the indirect effect and its significance (instead of the "covariance-reduction-perspective". The significance can be evaluated by the Sobel equation or, better, by means of bootstrapping.

An even better alternative would be to move away from regression analysis and test mediation where it belongs--in a full SEM. The reason is (see here a thread about the difference between SEM and regression: https://www.researchgate.net/post/What_is_the_difference_between_a_regression_analysis_and_SEM ):

Mediation in a regression framework does not deliver a good support for the (causal) mediation concept: As regression does not allow to include causal assumptions by means of fixing certain effects, the model is saturated (=partial mediation). The consequences are a) a huge number of equivalent models (around 40!)- that is, you can flip the arrows without noting any difference (see the papers by Kline and Thoemmes below) and b) no test of the assumptions. In a SEM you can fix the direct effect (if this is reasonable) and specify a larger set of predictors of the involved variables (e.g., instruments). This can narrow down the possibilities of equivalent models dramatically.

And yes, scientists are human and keep doing things despite improvements and/or shortcomings.

Best,

Holger

Kline, R. B. (2015). The mediation myth. Basic and Applied Social Psychology, 37(4), 202-213. doi:10.1080/01973533.2015.1049349

Thoemmes, F. (2015). Reversing arrows in mediation models does not distinguish plausible models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351

Dear Holger Steinmetz

Thank you for your prompt reply and guidance.

Regards,

Alireza

Many thanks for all of you colleagues..

Dr. Holger Steinmetz

Thank you so much for your valuable reply. I really used preacher and Hayes 2008 mediation approach which focus on

1- Bootstrap the Indirect effect (Total effect)

2- Bootstrapped Confidence Interval (Lower and upper level)

I recommend the free statistical program jamovi that allows mediation and moderation with several predictors in a simple way.

Thank you

Hi Christian,

Jamovi is surely a nice easy method to do many things and estimating the indirect effect with bootstrapping is the way to go. Unfortunately, the caveat still is its regression basis and that you *presume* (and not test) whether the mediation structure is correct.

For instance if the true model is not X --> M --> Y but X Y (i.e., the supposed mediator is a confounder), you get an effect of X (that is nonsense) and an indirect effect (which is nonsense too). If you are lucky to have an instrument for X (that is, a predictor of X that could help to reveal the true model) and you simply control for that instrument, the bias of X on M explodes and with it the indirect effect. That is one of the examples where controlling does more harm than good.

Overall, the strength of support for an indirect rises with

+1 Full mediation vs. partial mediation

+2 Instrumenting X

+3 Instrumenting X and M

You can do this with 2SLS but not OLS (perhaps this is possible in Jamovi?).

Best,

Holger

Thank you Prof for clarifying this approach..

Holger Steinmetz , I'm interested if you have any thoughts about the mediation package (https://cran.r-project.org/web/packages/mediation/index.html) and the work behind it (e.g. https://imai.fas.harvard.edu/projects/mechanisms.html).

Hi Daniel Wright ,

I have not worked with the package yet but know a bit about the approach and how it differs from traditional and modern approaches. Basically the Imai-approach addresses two important issues:

a) The theoretical roots is the potential outcome (PO) framework (by Donald Rubin) and not the SEM/graph theory framework (by Sewell Wright, Judea Pearl). Although Pearl again and again stresses that the potential outcome framework is equivalent to the graph theoretical framework, disciples of Rubin reject these claims. You will see the focus on the PO framework in their papers when all causal effects and mediation effects are defined in terms of differences in the potential outcomes of a treatment ("the effect of the treatment IF the treatment would be applied to individual i"). This leads to all these difficult to understand PO notations, for instance Yi(1) ("the potential outcome in Y for i IF treatment would be = 1"). The whole set of causal assumptions is represented in terms of complicated PO notations.

With regard to mediation, they treat the same assumptions behind a causal mediation effect about which I wrote in my initial message, for instance "sequential ignorability"--that is, no confounding of the X-M effect, X-Y effect and M-Y effect. But the PO parlance makes it hard to follow these rules. The graph approach in which I tend to invest my time, in contrast, makes all of that much more simple. You have to understand the 3 path tracing rules and the d-separation concept and you are equipped with powerful tools (although this will often result in a rather pessimistic conclusion of real chances to identify effects). Here is a short piece by Pearl addressing Imai and the equivalence between their approaches: https://ftp.cs.ucla.edu/pub/stat_ser/r421-reprint.pdf

In that paper, he also attacks the Baron-Kenny model BTW ;) And he gives a nice example in which cases "controlling for M" (Baron-Kenny) messes things up (namely when there is a confounding of the M-Y-link)

b) The second point is their generalization to non-linear models, for instance with binary or count mediators / outcomes. This is indeed a good point and this is also an important differentiation between Pearls approach (focusing on "structural causal models", SCM) and classical SEM: Whereas SCM is valid for all kinds of parametric and non-parametric models, traditional SEM is applicable to linear, parametric models. Indeed, this is a advantage of the approaches (although I think that this works 90% of the time). Although SEM provides some workarounds (e.g., by using different estimators, this kind of estimation treats, e.g., categorical variables as mere coarse measures of a true underlying continuous latent response variable (and not as a variable in itself), hence the estimated effects do reflect still effects among continuous variables--not the categorical variables.

I have only recently started to spend some time on non-parametric approaches such as GAMs and find that very fascinating (especially in big data situations in which you often have much larger scales (beyond the 5 point Likert scales :) which makes nonlinearity more plausible.

To cut a long story short

a) Imai is the same as Pearl (--> a causal perspective on mediation and suggestions how to approach it beyond regression)

b) Both differ from classical SEM by the generalizability to nonlinear models

HTH

Holger

Thanks Holger Steinmetz , that was very useful!!!