# Likert scale 0-4 or 1-5

I am conducting a study with Likert scale questions and my thesis advisor advised me to rescale the answers from 1-5 (strongly agree-strongly disagree) to 0-4. She says this will help in the regression analyses. I am researching the effect of a supportive manager on motivation of a employee (which are both Likert scale questions).

I do not understand the advantage of rescaling the model to 0-4. Does anyone know why this would be better?

• Regression of one ordered (ordinal) scale on another is a dubious idea any way. If you are proposing literally a regression of $y$ against $x$ subtracting 1 from the response just affects the intercept. it can't make interpretation easier. You need to widen the advice you're getting. Jul 8 '20 at 11:41

I don't understand it, either.

If you plot motivation (vertically) against manager supportiveness (horizontally), then rescaling only results in a relabeling of the axes: every 1 becomes a 0, every 2 a 1, and so on. (Incidentally, if you plot raw scores, you will have overplotting. Look into jittering your data to reduce this, or into sunflowerplots.)

If you regress motivation ($$y$$) on supportiveness ($$x$$), then the original regression equation might be

$$y=\beta_0+\beta_1x +\epsilon,$$

whereas the equation after rescaling would be

$$y'=\beta_0'+\beta_1'x'+\epsilon.$$

Now, $$y'=y-1$$ and $$x'=x-1$$, so the second equation becomes

$$y-1=\beta_0'+\beta_1'(x-1) + \epsilon,$$

or

$$y=1+\beta_0'-\beta_1'+\beta_1'x +\epsilon.$$

Comparing coefficients gives us

$$1+\beta_0'-\beta_1' = \beta_0\text{ and }\beta_1'=\beta_1.$$

Thus, the intercept changes, but the regression coefficient stays the same. (So will their $$t$$ and $$p$$ values.) The information content is precisely the same.

The only advantage I see is that the rescaled intercept coefficient is slightly easier to interpret, as motivation when supportiveness is zero - which is a valid value after rescaling, but not before. So it's not that the regression will be easier, but interpretation may be so, slightly.

You may want to ask your supervisor what they mean. Be prepared to tactfully change the subject if they start stuttering. Not everyone is (or needs to be) an expert in statistics.