Rate Ratio (RR)

Effect measure of Poisson and negative binomial regression — factor by which the expected count changes per unit of X.

Also known as: rate ratio, RR, incidence rate ratio, IRR

The rate ratio is the exponentiation of a regression coefficient $β_{j}$ in a log-link GLM (Poisson / negative binomial). It describes the multiplicative effect of a predictor on the expected event rate.

RR_{j} = e^{β_{j}} = \frac{E [ Y ∣ X _{j} = x + 1 ]}{E [ Y ∣ X _{j} = x ]}

RR = 1 — no effect
RR > 1 — X raises the expected count (RR = 1.3 → 30 % more events per unit of X)
RR < 1 — X lowers the expected count
Significance: the confidence interval must not contain 1

Used in

Regression (Attributive)

In the Algorithm Lab

regression/poisson-regression
regression/negbin-regression

Sources

Cameron, A. C. & Trivedi, P. K. — Regression Analysis of Count Data, 2nd Edition, Cambridge University Press
Hilbe, J. M. — Modeling Count Data, Cambridge University Press

Rate Ratio (RR)

See also

Used in

In the Algorithm Lab

Sources