# Can a single dummy variable be made to meet multiple criteria?

Let say I have criteria $$1, 2, 3,$$ and $$4$$. I would like the Dummy variable to be 1 only if a certain minimum amount of criteria are met. For example, if $$3$$ of the $$4$$ are true, then Dummy$$=1$$. If $$4$$ of the $$4$$ are true, then Dummy$$= 1$$. But if only $$1$$ or $$2$$ are true Dummy$$= 0$$.

What would be the theory / practical / research to refer to that decide how much of this criteria is enough to meet for the dummy to be $$1$$? Possible readings that you have seen this applied in would also be welcome.

The dummy application is in a regression model.

• You would look at the indicator function over the sets representing your criteria being satsified. If you want multiple ones to be satisfied you look at the indicator over intersections of such sets. I assume that your dummy variable is 0 or 1. Commented Jan 21 at 7:13
• Yes the dummy would be 0 or 1. On what framework / theory / model etc is 'enough' intersections (criteria met) determined? If 5 out 5 criteria are met, then it is easy to say the dummy should be 1. But for example, if 4 out of 5 criteria are met, how can I say that is enough to make the dummy value 1? By extension, why would 4 out of 5 be enough to assign 1 but not 3 out of 5?
– MLux
Commented Jan 22 at 11:12
• I do not think that there is a general theory because it is context dependent. In particular based on your application, you could have one where 1 our of 100 criteria is sufficient and another one where you need 99 out of 100. Commented Jan 22 at 11:24

As it was answered in the comments, there are no general criteria for how "large" the set (event) should be to construct a valid dummy variable, as this is context-dependent and not a mathematical question (mathematically, you can define an indicator function on the empty set $$\emptyset$$). However, from a practical perspective, this is an important question since you want to obtain a valid and stable coefficient estimator corresponding to your dummy variable. Therefore, when defining a dummy variable, you need to check that enough observations meet your criteria (whatever your criteria are). How much is enough? Well, it depends on the statistical power and (in)stability that you like to achieve (or tolerate). This is a statistical question where, under certain assumptions, you can compute the minimal sample size you need to meet your statistical criteria (e.g., minimal test power).