Mistake found: GAMs in a nutshell

[StevenWallaert]

Which page(s) do this mistake(s) pertain to?
GAMs in a nutshell
https://environmentalcomputing.net/statistics/gams/

Describe the error(s)

EnvironmentalComputing/content/Statistics/gams
/_index.rmd
lines 41 and 42

Describe a potential solution
$$ln(\lambda) = \beta_0 + f(x_1) , \quad y \sim Poisson(\lambda)$$

$$ln(\lambda) = \beta_0 + f(x_1) + z_1\gamma, \quad y \sim Poisson(\lambda), \quad \gamma \sim N(0,\Sigma)$$

[wcornwell]

good point, and sorry for the very slow reply. I think I see what you mean. Have corrected it so that:

• The link function connects the linear predictor to the mean $\lambda$, not the raw response $y$

• There is no additive error term $\varepsilon$ — the randomness is captured entirely by the distributional assumption $y \sim \text{Poisson}(\lambda)$