Converting a scaled variable

[Nae Khar]

Hello all,

I have a scale that rates each countries institutional quality from -2.5 to +2.5.

Is it true that this scale can impact my results negatively if used as it is in the analysis and that it should be converted/logged?

If so, how can I convert it to in order to avoid having it mess up my results?

Thanks in advance

[Nick Cox]

What negative impact do you fear? If this is how the data arrive, and you don't have any control over them, that should be fine, subject to all the usual concerns about measurement validity and reliability and about how much this variable will help your project.

Taking logarithms is out of the question as you have some negative values, and possibly some zeros too. I'd guess wildly that no other transformation will be either needed or useful.

[Nae Khar]

Thanks for your response.

I regret that I do not recall the specific details of why the scale ought to be converted, but I do remember being in an econometrics seminar where this was once suggested.

I am using that variable in a fixed effects regression with time and country FE.

I did notice that when using the percentile rank version of this same variable (ranking countries 1-100 instead of measuring them on a scale of -2.5 to +2.5), I get slightly different results.

I just wanted to make sure that maintaining the variable as is would not bias my results in any way.

[Nick Cox]

Again, why would that be a source of bias?

Percentile rank and any measured scale would only give the same results if data were all distinct values equally spaced.

[Nae Khar]

I appreciate the clarification.

I do not recall the theoretical underpinnings for why variables were suggested to be modified in some cases.

I was wondering whether someone in the forum has heard of something similar.

What I do recall is that in some instances, variables are logged (if they are highly skewed / not normally distributed) before inputting in a model, and that some scales are suggested to be converted.

[Nick Cox]

Naturally, some variables may be better logged -- although getting closer to linearity and additivity is a bigger deal than dealing with asymmetry -- but not any variable with scores like yours.

[Nae Khar]

Many thanks for addressing my concern.