library(knitr) options(knitr.kable.NA = '') options(digits = 2) knitr::opts_chunk$set(comment = ">") if (!requireNamespace("parameters", quietly = TRUE) || !requireNamespace("rstanarm", quietly = TRUE) || !requireNamespace("bayestestR", quietly = TRUE) || !requireNamespace("ppcor", quietly = TRUE)) { knitr::opts_chunk$set(eval = FALSE) } library(effectsize)

**Obtaining indices of effect size for Bayesian model is currently an issue**, as no test statistics are present to help us compute such indices. The two alternatives (both available in **effectsize**) is 1) to compute **standardized parameters** or 2) obtain effect sizes by **test-statistic approximation**. This second method is described here.

library("ppcor") df <- iris[, 1:4] # Remove the Species factor ppcor::pcor(df)$estimate[2:4, 1] # Select the rows of interest

The goal is to retrieve coefficients similar to the above **(partial) correlations** for this multiple regression model: `Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width`

. This can easily be achieved for frequentist models by converting the *t* statistic into a correlation:

library(effectsize) library(parameters) model <- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, data = df) parameters <- model_parameters(model)[2:4,] convert_t_to_r(parameters$t, parameters$df_residual)

Note that these are *not* equivalent to *standardized parameters* from multiple regressions (from which coefficients can be higher than 1).

standardize_parameters(model)$Std_Coefficient[2:4]

Let's start by fitting the Bayesian regression:

library("rstanarm") model <- stan_glm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, data = df)

library("rstanarm") model <- stan_glm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, data = df, refresh = 0, chains = 2)

The **effectsize** package provides the `posteriors_to_r()`

function, which attempts to estimate the posterior of the (partial) correlation coefficient by approximating the *t* statistic (deviding the coefficient by the SD of the posterior) and using frequentist degrees of freedom. It is an hybrid method that needs to be validated. However, the results appear as very close:

library(bayestestR) r <- convert_posteriors_to_r(model) bayestestR::describe_posterior(r)$Median[2:4]

Does it work in all cases?

Let's start with the frequentist model:

model <- glm(vs ~ cyl + disp + drat, data = mtcars, family = "binomial") parameters <- model_parameters(model) parameters$r <- convert_z_to_r(parameters$z, n = insight::n_obs(model)) parameters

However, as logistic models return log-odds, these can be directly converted to *r*:

parameters$r_from_odds <- convert_odds_to_r(parameters$Coefficient, log = TRUE) parameters

And now the Bayesian:

model <- stan_glm(vs ~ cyl + disp + drat,, data = mtcars, family = "binomial") parameters <- model_parameters(model) r <- convert_posteriors_to_r(model) parameters$r <- bayestestR::describe_posterior(r)$Median parameters$r_from_odds <- convert_odds_to_r(parameters$Median, log = TRUE) parameters

model <- stan_glm(vs ~ cyl + disp + drat,, data = mtcars, family = "binomial", refresh = 0) parameters <- model_parameters(model) r <- convert_posteriors_to_r(model) parameters$r <- bayestestR::describe_posterior(r)$Median parameters$r_from_odds <- convert_odds_to_r(parameters$Median, log = TRUE) parameters

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