Interpreting odds ratios as percentages?

Question

##                 OR  
## (Intercept) 0.0185 
## gre         1.0023 
## gpa         2.2345 
## rank2       0.5089 
## rank3       0.2618 
## rank4       0.2119

This output table is from https://stats.idre.ucla.edu/r/dae/logit-regression/. And the interpretation of the OR is as follows "for a one unit increase in gpa, the odds of being admitted to graduate school (versus not being admitted) increase by a factor of 2.23". My question is can I interpret "by a factor of 2.23" as "for a one unit increase in gpa, the chances of being admitted to graduate school is 223%"? i.e there's a 113% increase in being admitted?

Related: Interpretation of simple predictions to odds ratios in logistic regression. — gung - Reinstate Monica, Apr 28 '15 at 19:06
What you want is the fractional odds = Odds-1, i.e. 2.23-1, multiplied by 100 to be expressed as a percentage increase 123%. It would then be interpreted: "for a one unit increase in GPA, the chances of being admitted to graduate school increase by 123%". — Digio, Sep 08 '18 at 09:54

score 3 · Accepted Answer · answered Apr 28 '15 at 19:46

No.

First off, the odds can be used similarly to probability, but it is not quite the same. Odds of 1 to 10 or simply 1/10 (or 0.1) means that the probability of being admitted is one tenth of the probability of not being admitted. In other words, Prob(admit) = 1/11, prob(reject) = 10/11.

Note: Prob(admit) = odds/(1+odds).

The coefficient on GPS means that "for a one unit increase in gpa, the odds of being admitted to graduate school (versus not being admitted) increase by a factor of 2.23", in my example from 0.1 to 0.223. So now the probability of being admitted is 0.223/(1 + 0.223) = 0.182. So the probability of being admitted has approximately doubled, but it must, of course, be no larger than 1.

Interpreting odds ratios as percentages?

1 Answers1