# Objective

• To test which base of power performs best in the adaptation process [of something] in a buyer-supplier relationship

To understand that, I shall give a quick explanation about what bases of power are: French and Raven (1959) developed five bases of power:

1. Reward power is based on the influenced entity's perception that the influential entity "has the ability to mediate rewards for him".
2. Coercive power is based on the influenced entity's perception that the influential entity "has the ability to mediate punishments for him".
3. Legitimate power is based on the influenced entity's perception that the influential entity "has a legitimate right to prescribe behavior for him".
4. Referent power is based on the desire of the influenced entity to be associated with the influential entity.
5. Expert power is based on the influenced entity's perception that the influential entity "has some special knowledge or expertness" which is either useful or necessary for him.

The bases of power can be categorized in hard and soft bases of power. Let's say:

======================
Soft        Hard
----------------------
Expert      Coercive
Referent    Legitimate
Expert
======================


## Hypotheses

Now I want to find statistical support for the following hypotheses building on this framework:

H1a: The stronger a supplier depends on its buyer, the higher the likelihood to experience hard power bases.

H1b: The less a supplier depends on its buyer, the higher the likelihood to experience soft power bases.

H2a: A supplier experiencing a hard power base is likely to adapt a buyers [something] on request.

H2b: A supplier experiencing a soft power base is likely to refuse a buyers [something] on request.

# The approach

Now since I assume that there is a causal relation between the four variables I have, I understand mediation suitable to test the hypotheses H1a-H2b (Hayes, 2009). Therefore I created the following model which I want to test (assume there were no problems with measurement, validity and implementation in a statistical software).

## Model

                (Soft [M1])
/      \
/        \
/          \
(Dependence [X]). . . (Adaptation[Y])
\         /
\       /
\     /
(Hard [M2])


(I didn't know how to draw arrows in the model.)

# Question

Is it sensible to test the hypotheses in this way or would a linear structural equation model do the same job?

Follow up questions have to do with the implementation in R due to having two mediators; but before that it would be interesting for me, as a beginner in quantitative research, to hear whether this approach makes sense.

# References

French Jr., J. R. P., Raven, B., 1959. The Bases of Social Power. Ann Arbor; University of Michigan Press, Ch. 20, pp. 259–270

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

edit: If the question is not suitable for the CrossValidated group I would like to ask the admins to move it to the best fitting forum, or just delete.

The type of model you are describing has been referred to by Hayes (2003) as a parallel mediation model; you have multiple mediators, but no presumed temporal order for any of them in the causal chain between X and Y. The approach you have described is sensible, though I am not as familiar with R packages for running these sorts of multi-mediator roles (Hayes has a macro called PROCESS for SPSS and SAS).

However, your question seems to see this approach as a juxtaposed alternative from an SEM-based approach. In truth, you could fit the very same parallel mediation model using SEM--either using the observed variables in your model, or latent variables if that were preferable. This would be quite easy to do using the lavaan package, and you could also get bootstrapped estimates of your individual indirect effects. Some sample code for how you could do this (using observed, not latent variables) is below:

#Call the lavaan package
library(lavaan)

#Specify the parallel mediation model
med.model<-'
#direct effect

#mediator 1
soft~a1*dependence

#mediator 2
hard~a2*dependence

#indirect effects
ab1 := a1*b1
ab2 := a2*b2

#total effect
total := c + (a1*b1) + (a2*b2)
'

#Fit med.model to data frame "dat", and request bootstrapped standard errors
med.model.fit<-sem(med.model, data=dat, se = "bootstrap")

#Request summary output
summary(med.model.fit)