C21. A log-link coefficient

Topic: Standard errors, and models for counts · more questions on this topic
‹ Question 19 C22 ›

In a Poisson regression with a log link and no interactions, what does e^{\beta_j} represent?

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Definitions/notation. In \log\mu=x^\top\beta, \mu is the expected count and \beta_j is the coefficient of predictor x_j, with no interactions involving it. Holding other predictors fixed, a one-unit increase in x_j multiplies the expected count by e^{\beta_j}, a 100(e^{\beta_j}-1)\% change; this is an association, not automatically a causal effect.