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.
