Reading a log-linear coefficient
Section of Standard errors, and models for counts, part of Generalised linear models
Reading a log-linear coefficient
| Type | Section |
| Taught in | Standard errors, and models for counts |
| Part | Generalised linear models |
Two covariates are enough: \log\mu=\beta_0+\beta_1 x_1+\beta_2 x_2. Increase x_1 by one unit and hold x_2 fixed. The mean is multiplied by e^{\beta_1}. The same sentence with the labels swapped is \beta_2. The intercept is the mean when every covariate is at its baseline, \exp(\beta_0), and it is meaningful only when that baseline is a real situation. Do not judge a slope by whether the coefficient looks small. A small coefficient may be a large effect written in a small unit, and the comparison that matters is with the standard error.
Used in
See also
Standard errors in a GLM · Binomial counts in a GLM · Count responses · Quasi-Poisson · Mine-injury data · Count models beyond the Poisson · Overdispersion · Underdispersion