# How to create interaction variables from fractional response variables, i.e., response between 0 to 1 (shares/percentages)

I am wanting to use an interaction variable in the model. My independent variables are all in fractional form, i.e., between 0 and 1., but what I see online is all about binary/continuous variables. Are interaction variables only possible in these two cases? How do I create interaction variables for fractional response variables? and what will be their interpretation in the model?

For example: I have two categories of farms, 1. by type (dairy, field crop, horticulture, etc.), 2. by size (small, medium, large). Now, I want to make interaction variables, let's say, for horticulture and large farm size.

Could you please explain, how to do that? And how would you interpret its coefficient in the regression?

A "fraction" is never distinguished from a continuous variable. Interaction variables are created much the same way, as a product of the two lower-level variables.

The only considerations really apply to how the lower level variables are encoded in the regression model. Mainly, a "unit" difference doesn't make sense. Such a difference compares groups with exactly 0% to groups with exactly 100%. You can however, transform the variables to compare a 10% difference or 5% or 1% difference. The model predictions and inferences should all be the same. Lastly, the inferences can be wildly biased if the denominator of the "fraction" is a random quantity. The informative article "Fallacy of the Ratio" by Kronmal (approx 1993) is an illuminating read on this topic.

• I am interested in marginal effects. So basically, it's the unit change in share of X affecting the likelihood of the unit change in share of Y. Jun 28, 2021 at 15:52
• @KaptainAbid what you call a "unit" is somewhat arbitrary; it can be whatever you want it to be, provided you describe it in the methods. Scale proportions by 20 so that a "unit" is a 5% difference. Once the lower level variables are encoded, the interaction should probably maintain that scale for consistency. Jun 28, 2021 at 15:53
• alright. so, is it a requirement to keep both the original variables in the regression too? for example: if i make an interaction variable such that, the share of horticultural farms X share of large farms. Do i need to include both of these variables? P.S. the data is a panel data, consiting of 27 countries, over a period of 5 years, and i am using fractional probit because all the IVs and DV are in fractional form. Jun 28, 2021 at 15:57
• @KaptainAbid absolutely, you always keep the lower-level terms in when fitting the interaction, otherwise the interpretation of effects is just mind bending (as if standard interaction interpretation isn't hard enough). The goal is that the product term has a coefficient with an interpretation as a difference in differences. Jun 28, 2021 at 16:10