diff --git a/gen_linear_regression/beta.qmd b/gen_linear_regression/beta.qmd index ec35583..c95205d 100644 --- a/gen_linear_regression/beta.qmd +++ b/gen_linear_regression/beta.qmd @@ -27,12 +27,12 @@ The [logit](https://en.wikipedia.org/wiki/Logit) function is the quantile functi - $\beta$ (predictor weights) - $\kappa$ (concentration parameter) -The larger the value of $\kappa$, the more concentrated the distribution is around the mean. This parameter is also named the precision parameter or the sample size parameters. Greek letters $\nu$ and $\phi$ are also commonly used to refer to this parameter. +The larger the value of $\kappa$, the more concentrated the distribution is around the mean. This parameter is also named the precision parameter or the sample size parameter. Greek letters $\nu$ and $\phi$ are also commonly used to refer to this parameter. ## Prior for $\kappa$ -For weakly informative prior we can use a gamma distribution with low probability mass on very small values of $\kappa$, such priors disfavors u-shaped beta distributions which are generally less common in real-world data. For instance we could choose $\text{gamma}(4, 0.1)$ as discussed by [Solomon Kurz](https://solomonkurz.netlify.app/blog/2023-06-25-causal-inference-with-beta-regression/), wich place most of the prior mass on the double-digit range with long right tail allowing for greater concentrations if needed. +For weakly informative prior we can use a gamma distribution with low probability mass on very small values of $\kappa$, such priors disfavor u-shaped beta distributions which are generally less common in real-world data. For instance, we could choose $\text{gamma}(4, 0.1)$ as discussed by [Solomon Kurz](https://solomonkurz.netlify.app/blog/2023-06-25-causal-inference-with-beta-regression/), which place most of the prior mass on the double-digit range with long right tail allowing for greater concentrations if needed. ## See also @@ -42,4 +42,4 @@ For weakly informative prior we can use a gamma distribution with low probabilit - [Stan Functions Reference](https://mc-stan.org/docs/functions-reference/continuous_distributions_on_0_1.html#beta-distribution) - [rstanarm manual](https://mc-stan.org/rstanarm/articles/betareg.html) - [bambi manual](https://bambinos.github.io/bambi/notebooks/beta_regression.html) -- [Andrew Wheiss' blog](https://www.andrewheiss.com/blog/2021/11/08/beta-regression-guide/) \ No newline at end of file +- [Andrew Wheiss' blog](https://www.andrewheiss.com/blog/2021/11/08/beta-regression-guide/)