Indicator with three values

Question

I wanted to ask whether it can make sense to include a variable in a regression model that is coded in the following way?

• -1: something bad

• 0: something neutral

• 1: something good

The alternative of using a "good" and a "bad" dummy predictably runs into multicollinearity problems. Also, I am wondering what model would be appropiate in case I use such a variable as dependent variable? Thank you very much!

Best wishes, Felix

Answer 1

You are talking about defining your latent variable in terms of sign function. If it "makes sense" it depends on what exactly do you want to do and with what data, but there is no reason why you shouldn't use it in your model. You can start with the Why is gender typically coded 0/1 rather than 1/2, for example? thread that discusses different kinds of coding of variables.

People commonly use two kinds of coding of variables:

• 0 vs 1; that leads to $\beta \times 0 = 0$ and $\beta \times 1 = \beta$ estimates of effects for both levels,
• -1 vs 1; that leads to $\beta \times -1 = -\beta$ and $\beta \times 1 = \beta$ estimates of effects for both levels.

In your case your variable would lead to decrease by constant $-\beta$ for the "bad" level, would have no effect with the "neutral" level and would increase the predictions by constant $\beta$ for the "good" level.