diff --git a/gen_linear_regression/gamma.qmd b/gen_linear_regression/gamma.qmd new file mode 100644 index 0000000..e88f50b --- /dev/null +++ b/gen_linear_regression/gamma.qmd @@ -0,0 +1,24 @@ +--- +title: Gamma model +--- + +## Description + +Linear regression with gamma distributed residuals. + +## Definition + +For continuous outcome $y$ lower bounded at zero and predictors $x$, the model is: + +$$ +\begin{align} +y_i \sim \text{gamma}(s, \alpha/exp(\eta)) \\ +\eta_i = \alpha + \beta \cdot x_i +\end{align} +$$ + +## Parameters needing priors + +- $\alpha$ (intercept) +- $\beta$ (predictor weights) +- $s$ shape parameter