From 2abbfb58179f658395310f71f4192cb1bae28d61 Mon Sep 17 00:00:00 2001
From: n-kall <33577035+n-kall@users.noreply.github.com>
Date: Fri, 13 Sep 2024 11:27:33 +0300
Subject: [PATCH] start adding gamma regression

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 gen_linear_regression/gamma.qmd | 24 ++++++++++++++++++++++++
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 create mode 100644 gen_linear_regression/gamma.qmd

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+---
+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