Categorical Moderator with four categories

[jmerk]

Dear smartPLS-community,

I have a question regarding the a moderation analysis with a categorical moderator.

My model consists of 5 independent variables (higher-order constructs) and 3 dependent variables of which one is a a higher-order construct as well. In addition to the relationship between the IVs and DVs, I am interested in the moderator effect of "corporate culture". In my study, corporate culture can be one of four culture types, equivalent to the four treatment groups of my study. Unfortunately, I am not sure how to include the moderator in my model.

My first approach was to include three binary variables in the model (culture type 1 = yes/no; culture type 2 = yes/no, culture type 3 = yes/no) and the fourth culture type would then be the reference group. But then I am not entirely sure how to interpret the interaction terms and I don't know whether there is a difference for instance between culture type 2 and 3.

Any help or recommendation is highly appreciated!

[jmbecker]

The binary variable approach is one possibility, but as you say it has the downside of only estimating changes relative to the reference group.
In such a situation, the "direct" simple effect is the effect in the reference group and the interaction effects are the changes in the effect when switching from the reference group to the focal group.
(also see our discussion of binary moderation in Becker, J.-M., Cheah, J.-H., Gholamzade, R., Ringle, C.M. and Sarstedt, M. (2023), "PLS-SEM’s most wanted guidance", International Journal of Contemporary Hospitality Management, Vol. 35 No. 1, pp. 321-346. https://doi.org/10.1108/IJCHM-04-2022-0474)

In principle you could create several models, and use different reference categories in each model to understand the differences between all groups. The problem is that you would need to account for multiple testing somehow (e.g., Bonferroni correction or something similar).

An typical alternative to the binary variable approach would be a multi group analysis (MGA). There you will get the effect for each group and then you can go into direct pairwise comparisons to understand the differences. Again, you would need to account for multiple testing (e.g., Bonferroni correction or something similar).
In addition, a problem (but also an advantage) can be that you estimate all parameters to be group-specific and not only the focal effect. This can show heterogeneity in other parts of the model, but may also complicate your discussion.
This usually comes at the cost of being a less powerful approach, i.e., that it is harder to detect effect (differences) to be significant.