Odds Ratio (OR)

Standard effect measure of logistic regression — factor by which the odds $p / (1 - p)$ change per unit of X.

Also known as: odds ratio, OR

The odds ratio is the exponentiation of a regression coefficient $β_{j}$ in logistic regression. It describes how the odds $p / (1 - p)$ of $Y = 1$ change when $X_{j}$ rises by one unit — holding all other predictors constant.

OR_{j} = e^{β_{j}} = \frac{Odds ( Y = 1 ∣ X _{j} = x + 1 )}{Odds ( Y = 1 ∣ X _{j} = x )}

OR = 1 — no effect
OR > 1 — X raises the odds of $Y = 1$ (e.g. OR = 2.5: 2.5× the odds)
OR < 1 — X lowers the odds (e.g. OR = 0.4: 60 % lower odds)
Significance: the confidence interval must not contain 1

Used in

Regression (Attributive)

In the Algorithm Lab

regression/logistic-regression

Sources

Hosmer, D. W., Lemeshow, S. & Sturdivant, R. X. — Applied Logistic Regression, 3rd Edition, Wiley
Agresti, A. — Categorical Data Analysis, 3rd Edition, Wiley

Odds Ratio (OR)

See also

Used in

In the Algorithm Lab

Sources