What is a "unit change" in a regressor that is a continuous index with values between 0 and 1

[Kwasi Tabiri]

Hello Statalist!

I am working on a project where I am measuring employment precarity as a multidimensional index using the Alkire-Foster methodology. So each dimension has a weight w, and each dimension is made up of one or more indicators I. The indicators are dummies, equal to 1 if the individual is deprived in the indicator and 0 otherwise. Assuming there are 3 indicators, the multidimensional index is computed as

index = w₁I₁ + w₂I₂+ w₃I₃

This means that index is between 0 and 1. In terms of the my study, 0 means no employment precarity, and 1 means the individual is deprived in all the dimensions of precarity (which is rarely the case). My question is this: if I want to interpret the coefficient of index in a regression, would it be right to say a "unit increase" (from 0 to 1) in the index is associated with x units change in the outcome?

I am a bit confused because the index is continuous, and it may not be appropriate to consider a move from one end of the spectrum to another as a unit change.

Thanks for your help!

[Nick Cox]

A unit change is a unit change, minute if the range of a variable is enormously larger, ridiculous if considerably smaller. For that reason some people prefer considering the effect of say a change of 1 SD on each predictor. Contrariwise, a change of 1 SD for a (0, 1) predictor doesn't have an easy substantive description.

[Rich Goldstein]

I am not familiar with your jargon or your index at all - but leaving the index within the 0/1 range might well mean "outlandish" coefficients and I would consider multiplying the index by 100 prior to estimating a model

[Kwasi Tabiri]

Thank you for your comments. I have found that a way around this is to divide my index by 10. That way, a unit change can be interpreted as a 0.1 unit change in the index, which is not as ridiculous as moving from one end of the variable to another. Once again, I do appreciate your inputs.

Best,
Kwasi

[Daniel Schaefer]

Sorry, but I think you mean you will multiply your index by 10, correct - to get a number ranging from 0 to 10?

[Kwasi Tabiri]

Yes, that is correct. Thank you for the correction, Daniel!