Mediation: negative or positive coefficients?

[janssengr]

I can't wrap my head around the following, so any help is gladly appreciated.


I have a simple mediation model, but the mediator (M) "Asymmetry in Fairness Perception" is a difference-score variable.

mediation model.png (8.97 KiB) Viewed 8493 times

E.g. based on two 7-point Likert-type items, one for the focal firm, and one for its partner, I took the difference. So if the focal firm scored 4, and the partner scored 3, the difference would be 1. Similarly, focal firm 3 and partner 7 would result in -4. --> it looks a bit how Power/Dependence-studies have been carried out in the past (Casciaro and Piskorski 2005).

Now, if I estimate the model with the PLS algorithm and bootstrap routine, I obtain the coefficients and t-values noted in the image.
The IV-M coefficient of -0.211 sounds logical to me. Higher application of contracts leads to lower perceptions of fairness asymmetries.
However, the 0.253 puzzles me - I'd expect a negative coefficient there too. Now it reads: an increase in fairness asymmetries perceptions increases performance. The other way around would make more sense: an increase in fairness asymmetry perceptions decreases performance.

I tried using absolute values (like Casciaro and Piskorski 2005), but then the variable doesnt have any effect in the model anymore.

Does anyone have an idea, or am I making a mistake?

[jmbecker]

I would also think that an absolute value is more what you want to model for the mediator ("Asymmetry in Fairness Perception"), because any deviation from 0 indicates an asymmetry (both to the positive and negative side). Maybe there is no effect of fairness asymmetry? You may also think about a quadratic difference inteasd of absolute difference.

What you find at the moment is not that "Higher application of contracts leads to lower perceptions of fairness asymmetries.", but that higher application of contracts leads to an asymmetry where the focal firm has low perceived fairness and the partner high perceived fairness, i.e., the difference score reduces to zero or negative values if application of contracts increase. That is not what you want to model and probably the data structure might also confound effects.

There are some discussions whether difference scores are valueable or should be avoided. Edwards has a lot of matrial on this issues and seems to be a critic of the difference score approach. Maybe some of his arguments may help you solve your issues.

[janssengr]

Dear Dr Becker, I totally forgot to thank you.
Sorry about that, but you have helped me a lot in understanding my problem. I am now in process of solving it, using Edwards as a reference too. Thanks very much!

best regards,
Robbert

[sondes kacem]

Hello!
Please I would like more on mediation analysis method by the SMART PLS3, my model has a mulitidimensional independent variable, uni-dimensional mediating variable and multi dimensional dependent variable, how can I analyze mediation at each factor in my independent variable via the PLS, thank you

[jmbecker]

It depends on your multidimensional construct. If it is a reflective-formative (type II) model, it contains itself an inherent mediation hypothesis (that the higher-order construct fully mediated the effect of the lower-order constructs).
Hence, you would have a multiple mediator model. Yet, the most important part are the indirect effects. For total indirect effects, but you might have to calculate the focal effects yourself tracing the paths downstream to your DV.

[sondes kacem]

All the latent constructs are reflexive, I want know how I can analyze the mediation since my independent variable and the dependent variable are multidimensional, , how I'll check my assumptions?
The independant variable have 3 factors, each factors have a number of items
The dependant variable have 5 factors, each factor have a number of items
The mediator is multidimensional
the hypotheses
The mediator mediates the effect of factor 1 of IV on factor 1' of DV
The mediator mediates the effect of factor 1 of IV on factor 2' of DV
The mediator medaites the effect of factor 1 of IV on factor 3' of DV
The mediator mediates the effect of factor 1 of IV on factor 4' of DV
The mediator mediates the effect of factor 1 of IV on factor 5' of DV
The mediator mediates the effect of factor 2 of IV on factor 1' of DV
The mediator mediates the effect of factor 2 of IV on factor 2' of DV
The mediator mediates the effect of factor 2 of IV on factor 3' of DV
The mediator mediates the effect of factor 2 of IV on factor 4' of DV
The mediator mediates the effect of factor 2 of IV on factor 5' of DV
The mediator mediates the effect of factor 3 of IV on factor 1' of DV
The mediator mediates the effect of factor 3 of IV on factor 2' of DV
The mediator mediates the effect of factor 3 of IV on factor 3' of DV
The mediator mediates the effect of factor 3 of IV on factor 4' of DV
The mediator mediates the effect of factor 3 of IV on factor 5' of DV

Thank you