Updated 10/11/2021
Sometimes it makes sense to change the scale of predictor variables so that interpretations of parameter estimates, including odds ratios, make sense. It is generally done by multiplying the values of a predictor by a constant, often a factor of 10.
Since parameter estimates and odds ratios tell you the effect of a one unit change in the predictor, you should multiply them so that a one unit change in the predictor makes sense.
Here is a really simple example that I use in my logistic regression workshop.
Y= whether or not a student goes on academic probation after the first semester in college
X1= high school GPA (measured on a 4 pt scale)
X2=SAT score
If you don’t multiply either predictor, neither makes sense. A one-unit change in GPA is huge– a .1 unit change makes much more sense.
Likewise, a one-unit change in SAT score is too small. In fact, the way the SAT is scored, you couldn’t have two SAT scores one unit apart–they go by 10’s.
In my (completely made up) example the odds ratio for SAT score is something like 1.03. Tiny, but significant, because a one-unit difference in SAT score is tiny. But if you divide SAT score by 10, 10 points becomes 1 unit, so the odds ratio is based on that scale.
Likewise, you could multiply GPA by 10 (essentially changing it from a 4 to a 40 point scale). Now a 1 unit change is meaningful.
If you want to learn all the ins and outs of interpreting regression coefficients, check out our 6-hour online workshop Interpreting (Even Tricky) Regression Coefficients. This workshop will teach you the real meaning of coefficients for all the tricky regression terms: correlated predictors, dummy variables, interactions, polynomials, and more.