### Install tidybayes.rethinking from GitHub

Source: https://mjskay.github.io/tidybayes.rethinking

Install the devtools package if you don't have it, then install tidybayes.rethinking from GitHub.

```r
install.packages("devtools")     # only necessary if you don't have devtools already
devtools::install_github("mjskay/tidybayes.rethinking")
```

--------------------------------

### Install tidybayes Development Version from GitHub

Source: https://mjskay.github.io/tidybayes/index.html

Installs the latest development version of the tidybayes package from GitHub using the devtools package.

```R
install.packages("devtools")
devtools::install_github("mjskay/tidybayes")
```

--------------------------------

### Example: Gather variables from tidy_draws and calculate median and QI

Source: https://mjskay.github.io/tidybayes/reference/gather_variables.html

This example shows how to use gather_variables with tidy_draws to reshape the data, followed by median_qi to compute median and quantile intervals. This is similar to ggmcmc::ggs.

```R
# the first three lines below are roughly equivalent to ggmcmc::ggs(RankCorr)
RankCorr %>%
  tidy_draws() %>%
  gather_variables() %>%
  median_qi()

```

--------------------------------

### Create Example Dataset

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

Generates a tibble with 5 conditions and 10 observations each, including random responses. This dataset is used to demonstrate tidybayes functionalities.

```R
set.seed(5)
n = 10
n_condition = 5
ABC =
  tibble(
    condition = factor(rep(c("A","B","C","D","E"), n)),
    response = rnorm(n * 5, c(0,1,2,1,-1), 0.5)
  )
```

--------------------------------

### Example: Gather variables and calculate median and QI

Source: https://mjskay.github.io/tidybayes/reference/gather_variables.html

This example demonstrates using gather_variables after spread_draws to reshape the data, then calculates the median and quantile interval for each variable. It requires dplyr and ggdist packages.

```R
# \donttest{

library(dplyr)

data(RankCorr, package = "ggdist")

RankCorr %>%
  spread_draws(b[i,v], tau[i]) %>%
  gather_variables() %>%
  median_qi()

```

--------------------------------

### Install tidybayes from CRAN

Source: https://mjskay.github.io/tidybayes/index.html

Installs the latest stable version of the tidybayes package from CRAN.

```R
install.packages("tidybayes")
```

--------------------------------

### Visualize Example Dataset

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

Creates a scatter plot of the 'response' variable against 'condition' to visualize the distribution of data points.

```R
ABC %>%
  ggplot(aes(x = response, y = fct_rev(condition))) + 
  geom_point(alpha = 0.5) +
  ylab("condition")
```

--------------------------------

### Example Dataset with Categorical Predictor

Source: https://mjskay.github.io/tidybayes/reference/recover_types.html

This example demonstrates creating a tibble with a categorical predictor variable that has multiple levels, which can then be used with `recover_types` to ensure correct type recovery.

```R
# Here's an example dataset with a categorical predictor (`condition`) with several levels:
set.seed(5)
n = 10
n_condition = 5
ABC = tibble(
  condition = factor(rep(c("A","B","C","D","E"), n)),
  response = rnorm(n * 5, c(0,1,2,1,-1), 0.5)
)
```

--------------------------------

### Load Required Libraries for Tidybayes Examples

Source: https://mjskay.github.io/tidybayes/index.html

Loads essential R libraries for data manipulation, visualization, and statistical modeling, commonly used with tidybayes.

```R
library(magrittr)
library(dplyr)
library(ggplot2)
library(rstan)
library(tidybayes)
library(emmeans)
library(broom)
library(brms)
library(modelr)
library(forcats)
library(cowplot)
library(RColorBrewer)
library(gganimate)

theme_set(theme_tidybayes() + panel_border())
```

--------------------------------

### Example: Extracting Draws from a Model Fit

Source: https://mjskay.github.io/tidybayes/reference/tidy_draws.html

This example demonstrates how to use `tidy_draws` to extract posterior draws from a model fit object. It requires the `coda` package for the `line` dataset and the `magrittr` package for the pipe operator.

```R
library(magrittr)

data(line, package = "coda")

line %>%
  tidy_draws()

```

--------------------------------

### emmeans contrast method example (eff)

Source: https://mjskay.github.io/tidybayes/reference/emmeans_comparison.html

Demonstrates the output of the 'eff' emmeans contrast method, which compares each level to the average of all levels. This matrix format is not directly usable by compare_levels.

```r
emmeans:::eff.emmc(c("a","b","c","d"))
```

--------------------------------

### Create Sample Dataset for Modeling

Source: https://mjskay.github.io/tidybayes/index.html

Generates a tibble named 'ABC' with 'condition' and 'response' variables, suitable for hierarchical modeling examples. Includes a basic ggplot visualization of the data.

```R
set.seed(5)
n = 10
n_condition = 5
ABC =
  tibble(
    condition = factor(rep(c("A","B","C","D","E"), n)),
    response = rnorm(n * 5, c(0,1,2,1,-1), 0.5)
  )

ABC %>%
  ggplot(aes(x = response, y = condition)) +
  geom_point(alpha = 0.5) +
  ylab("condition")
```

--------------------------------

### R Example: Extracting and Summarizing Marginal Means

Source: https://mjskay.github.io/tidybayes/reference/gather_emmeans_draws.html

Demonstrates how to fit a brms model, calculate marginal means by condition using emmeans, and then extract and summarize the posterior draws using gather_emmeans_draws and median_qi.

```R
# \dontrun{

library(dplyr)
library(magrittr)
library(brms)
library(emmeans)
#> Welcome to emmeans.
# > Caution: You lose important information if you filter this package's results.
# > See '? untidy'

# Here's an example dataset with a categorical predictor (`condition`) with several levels:
set.seed(5)
n = 10
n_condition = 5
ABC = tibble(
  condition = rep(c("A","B","C","D","E"), n),
  response = rnorm(n * 5, c(0,1,2,1,-1), 0.5)
)

m = brm(response ~ condition, data = ABC,
  # 1 chain / few iterations just so example runs quickly
  # do not use in practice
  chains = 1, iter = 500)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 5.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.53 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:   1 / 500 [  0%]  (Warmup)
#> Chain 1: Iteration:  50 / 500 [ 10%]  (Warmup)
#> Chain 1: Iteration: 100 / 500 [ 20%]  (Warmup)
#> Chain 1: Iteration: 150 / 500 [ 30%]  (Warmup)
#> Chain 1: Iteration: 200 / 500 [ 40%]  (Warmup)
#> Chain 1: Iteration: 250 / 500 [ 50%]  (Warmup)
#> Chain 1: Iteration: 251 / 500 [ 50%]  (Sampling)
#> Chain 1: Iteration: 300 / 500 [ 60%]  (Sampling)
#> Chain 1: Iteration: 350 / 500 [ 70%]  (Sampling)
#> Chain 1: Iteration: 400 / 500 [ 80%]  (Sampling)
#> Chain 1: Iteration: 450 / 500 [ 90%]  (Sampling)
#> Chain 1: Iteration: 500 / 500 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.012 seconds (Warm-up)
#> Chain 1:                0.006 seconds (Sampling)
#> Chain 1:                0.018 seconds (Total)
#> Chain 1: 

# Once we've fit the model, we can use emmeans() (and functions
# from that package) to get whatever marginal distributions we want.
# For example, we can get marginal means by condition:
m %>%
  emmeans(~ condition) %>%
  gather_emmeans_draws() %>%
  median_qi()
#> # A tibble: 5 × 7
#>   condition .value .lower .upper .width .point .interval
#>   <fct>      <dbl>  <dbl>  <dbl>  <dbl> <chr>  <chr>    
#> 1 A          0.191 -0.128  0.542   0.95 median qi       
#> 2 B          1.02   0.685  1.35    0.95 median qi       
#> 3 C          1.87   1.54   2.21    0.95 median qi       
#> 4 D          1.03   0.683  1.37    0.95 median qi       
#> 5 E         -0.948 -1.30  -0.584   0.95 median qi       

```

--------------------------------

### Example: Summarizing Draws Before and After combine_chains

Source: https://mjskay.github.io/tidybayes/reference/combine_chains.html

Demonstrates the effect of `combine_chains` on a tidy data frame of draws. The first summary shows the default `.chain` and `.iteration` columns, while the second shows the result after `combine_chains` has merged them into the `.draw` column.

```R
library(magrittr)
library(coda)

data(line, package = "coda")

# The `line` posterior has two chains with 200 iterations each:
line %>%
  tidy_draws() %>%
  summary()
#>
#>      .chain      .iteration         .draw           alpha      
#>  Min.   :1.0   Min.   :  1.00   Min.   :  1.0   Min.   :0.858  
#>  1st Qu.:1.0   1st Qu.: 50.75   1st Qu.:100.8   1st Qu.:2.732  
#>  Median :1.5   Median :100.50   Median :200.5   Median :3.019  
#>  Mean   :1.5   Mean   :100.50   Mean   :200.5   Mean   :2.988  
#>  3rd Qu.:2.0   3rd Qu.:150.25   3rd Qu.:300.2   3rd Qu.:3.242  
#>  Max.   :2.0   Max.   :200.00   Max.   :400.0   Max.   :7.173  
#>       beta             sigma        
#>  Min.   :-1.5662   Min.   : 0.3262  
#>  1st Qu.: 0.6039   1st Qu.: 0.6158  
#>  Median : 0.7963   Median : 0.7912  
#>  Mean   : 0.7992   Mean   : 0.9681  
#>  3rd Qu.: 0.9925   3rd Qu.: 1.0752  
#>  Max.   : 1.8320   Max.   :11.2331  

# combine_chains combines the chain and iteration column into the .draw column.
line %>%
  tidy_draws() %>%
  combine_chains() %>%
  summary()
#>
#>      .chain      .iteration         .draw           alpha      
#>  Min.   :1.0   Min.   :  1.00   Min.   :  1.0   Min.   :0.858  
#>  1st Qu.:1.0   1st Qu.: 50.75   1st Qu.:100.8   1st Qu.:2.732  
#>  Median :1.5   Median :100.50   Median :200.5   Median :3.019  
#>  Mean   :1.5   Mean   :100.50   Mean   :200.5   Mean   :2.988  
#>  3rd Qu.:2.0   3rd Qu.:150.25   3rd Qu.:300.2   3rd Qu.:3.242  
#>  Max.   :2.0   Max.   :200.00   Max.   :400.0   Max.   :7.173  
#>       beta             sigma        
#>  Min.   :-1.5662   Min.   : 0.3262  
#>  1st Qu.: 0.6039   1st Qu.: 0.6158  
#>  Median : 0.7963   Median : 0.7912  
#>  Mean   : 0.7992   Mean   : 0.9681  
#>  3rd Qu.: 0.9925   3rd Qu.: 1.0752  
#>  Max.   : 1.8320   Max.   :11.2331  



```

--------------------------------

### Generating Multimodal Draws for HDI Example

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

This code snippet generates sample data from a multimodal normal mixture distribution, which is then used to demonstrate the behavior of `mode_hdi()`.

```R
set.seed(123)
multimodal_draws = tibble(
  x = c(rnorm(5000, 0, 1), rnorm(2500, 4, 1))
)
```

--------------------------------

### Example: Plotting Posterior Predictive Intervals with add_draws

Source: https://mjskay.github.io/tidybayes/reference/add_draws.html

This example demonstrates how to use `add_draws` with `posterior_epred` to plot posterior predictive intervals for a brms model. It requires `ggplot2`, `dplyr`, `brms`, and `modelr` packages. Note that this usage is roughly equivalent to `add_epred_draws` but lacks argument standardization across model types.

```r
# \dontrun{

library(ggplot2)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(brms)
#> Loading required package: Rcpp
#> Loading 'brms' package (version 2.21.0). Useful instructions
#> can be found by typing help('brms'). A more detailed introduction
#> to the package is available through vignette('brms_overview').
#> 
#> Attaching package: 'brms'
#> The following objects are masked from 'package:tidybayes':
#> 
#>     dstudent_t, pstudent_t, qstudent_t, rstudent_t
#> The following object is masked from 'package:stats':
#> 
#>     ar
library(modelr)

theme_set(theme_light())

m_mpg = brm(mpg ~ hp * cyl, data = mtcars,
  # 1 chain / few iterations just so example runs quickly
  # do not use in practice
  chains = 1, iter = 500)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 3.7e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.37 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:   1 / 500 [  0%]  (Warmup)
#> Chain 1: Iteration:  50 / 500 [ 10%]  (Warmup)
#> Chain 1: Iteration: 100 / 500 [ 20%]  (Warmup)
#> Chain 1: Iteration: 150 / 500 [ 30%]  (Warmup)
#> Chain 1: Iteration: 200 / 500 [ 40%]  (Warmup)
#> Chain 1: Iteration: 250 / 500 [ 50%]  (Warmup)
#> Chain 1: Iteration: 251 / 500 [ 50%]  (Sampling)
#> Chain 1: Iteration: 300 / 500 [ 60%]  (Sampling)
#> Chain 1: Iteration: 350 / 500 [ 70%]  (Sampling)
#> Chain 1: Iteration: 400 / 500 [ 80%]  (Sampling)
#> Chain 1: Iteration: 450 / 500 [ 90%]  (Sampling)
#> Chain 1: Iteration: 500 / 500 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.187 seconds (Warm-up)
#> Chain 1:                0.044 seconds (Sampling)
#> Chain 1:                0.231 seconds (Total)
#> Chain 1: 
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess

# plot posterior predictive intervals
mtcars %>%
  group_by(cyl) %>%
  data_grid(hp = seq_range(hp, n = 101)) %>%
  # the line below is roughly equivalent to add_epred_draws(m_mpg), except
  # that it does not standardize arguments across model types.
  add_draws(posterior_epred(m_mpg, newdata = .)) %>%
  ggplot(aes(x = hp, y = mpg, color = ordered(cyl))) + 
  stat_lineribbon(aes(y = .value), alpha = 0.25) + 
  geom_point(data = mtcars) + 
  scale_fill_brewer(palette = "Greys")


# }

```

--------------------------------

### Basic Usage of gather_pairs for Scatterplot Matrix

Source: https://mjskay.github.io/tidybayes/reference/gather_pairs.html

Demonstrates how to use gather_pairs to create pairwise combinations for plotting. This example customizes output column names and generates a scatterplot matrix using ggplot2.

```R
library(ggplot2)
library(dplyr)

t_a = rnorm(100)
t_b = rnorm(100, t_a * 2)
t_c = rnorm(100)

df = rbind(
  data.frame(g = "a", t = t_a),
  data.frame(g = "b", t = t_b),
  data.frame(g = "c", t = t_c)
)

df %>%
  gather_pairs(g, t, row = "g_row", col = "g_col", x = "t_x", y = "t_y") %>%
  ggplot(aes(t_x, t_y)) +
  geom_point() +
  facet_grid(vars(g_row), vars(g_col))
```

--------------------------------

### Plotting posterior predictive lines with sampled draws

Source: https://mjskay.github.io/tidybayes/reference/sample_draws.html

This example demonstrates how to use `sample_draws` to select a subset of posterior draws for plotting. It's recommended to use `sample_draws` for spaghetti plots, but for plotting intervals, it's best to use all available draws.

```R
# \dontrun{

library(ggplot2)
library(dplyr)
library(brms)
library(modelr)

theme_set(theme_light())

m_mpg = brm(mpg ~ hp * cyl, data = mtcars,
  # 1 chain / few iterations just so example runs quickly
  # do not use in practice
  chains = 1, iter = 500)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 4e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.4 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:   1 / 500 [  0%]  (Warmup)
#> Chain 1: Iteration:  50 / 500 [ 10%]  (Warmup)
#> Chain 1: Iteration: 100 / 500 [ 20%]  (Warmup)
#> Chain 1: Iteration: 150 / 500 [ 30%]  (Warmup)
#> Chain 1: Iteration: 200 / 500 [ 40%]  (Warmup)
#> Chain 1: Iteration: 250 / 500 [ 50%]  (Warmup)
#> Chain 1: Iteration: 251 / 500 [ 50%]  (Sampling)
#> Chain 1: Iteration: 300 / 500 [ 60%]  (Sampling)
#> Chain 1: Iteration: 350 / 500 [ 70%]  (Sampling)
#> Chain 1: Iteration: 400 / 500 [ 80%]  (Sampling)
#> Chain 1: Iteration: 450 / 500 [ 90%]  (Sampling)
#> Chain 1: Iteration: 500 / 500 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.128 seconds (Warm-up)
#> Chain 1:                0.045 seconds (Sampling)
#> Chain 1:                0.173 seconds (Total)
#> Chain 1: 
#> Warning: The largest R-hat is 1.07, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess

# draw 100 fit lines from the posterior and overplot them
mtcars %>%
  group_by(cyl) %>%
  data_grid(hp = seq_range(hp, n = 101)) %>%
  add_epred_draws(m_mpg) %>%
  # NOTE: only use sample_draws here when making spaghetti plots; for
  # plotting intervals it is always best to use all draws
  sample_draws(100) %>%
  ggplot(aes(x = hp, y = mpg, color = ordered(cyl))) +
  geom_line(aes(y = .epred, group = paste(cyl, .draw)), alpha = 0.25) +
  geom_point(data = mtcars)


# }

```

--------------------------------

### Explicitly specify column for median_qi with grouped data

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

This is a more verbose equivalent to the previous example. It explicitly groups by `condition` (though `spread_draws` does this automatically) and then applies `median_qi` to the `condition_mean` column.

```R
m %>%
  spread_draws(condition_mean[condition]) %>%
  group_by(condition) %>%
  median_qi(condition_mean)
```

--------------------------------

### Compose Nested Data with x_at_y

Source: https://mjskay.github.io/tidybayes/reference/x_at_y.html

Use x_at_y to create a nested index for 'site' based on 'plot'. This example demonstrates turning a site identifier into a nested index where each plot maps to its corresponding site.

```R
library(magrittr)

df = data.frame(
  plot = factor(paste0("p", rep(1:8, times = 2))),
  site = factor(paste0("s", rep(1:4, each = 2, times = 2)))
)

# turns site into a nested index: site[p] gives the site for plot p
df %>%
  compose_data(site = x_at_y(site, plot))
```

--------------------------------

### Annotating Densities with stat_halfeye and fill aesthetic

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

The fill aesthetic in stat_halfeye can vary within a slab to annotate specific regions, such as a region of practical equivalence (ROPE). This example annotates the ROPE with a different color.

```R
m %>%
  spread_draws(condition_mean[condition]) %>%
  ggplot(aes(y = fct_rev(condition), x = condition_mean, fill = after_stat(abs(x) < .8))) +
  stat_halfeye() +
  geom_vline(xintercept = c(-.8, .8), linetype = "dashed") +
  scale_fill_manual(values = c("gray80", "skyblue"))
```

--------------------------------

### Animated Hypothetical Outcome Plots (HOPs)

Source: https://mjskay.github.io/tidybayes/articles/tidy-brms.html

Create animated hypothetical outcome plots (HOPs) of fit lines. This example uses a small number of draws for demonstration purposes.

```r
set.seed(123456)
# NOTE: using a small number of draws to keep this example

```

--------------------------------

### Fitting a Stan Model with tidybayes

Source: https://mjskay.github.io/tidybayes/reference/recover_types.html

Fits a Stan model using the `stan()` function and prepares data using `compose_data()`. Control parameters for adaptation are set, and the number of chains and iterations are reduced for a quick example.

```r
m = stan(model_code = stan_code, data = compose_data(ABC), control = list(adapt_delta=0.99),
  # 1 chain / few iterations just so example runs quickly
  # do not use in practice
  chains = 1, iter = 500)

```

--------------------------------

### Plotting Summarized Intervals with geom_pointinterval

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

This example demonstrates plotting summarized posterior intervals using geom_pointinterval. The linewidth aesthetic is mapped to -.width, so smaller probability intervals appear as thicker lines. This mapping is a default in geom_pointinterval when a .width column is present.

```R
m %>%
  spread_draws(condition_mean[condition]) %>%
  median_qi(.width = c(.95, .66)) %>%
  ggplot(aes(
    y = fct_rev(condition), x = condition_mean, xmin = .lower, xmax = .upper,
    # size = -.width means smaller probability interval => thicker line
    # this can be omitted, geom_pointinterval includes it automatically
    # if a .width column is in the input data.
    linewidth = -.width
  )) +
  geom_pointinterval()
```

--------------------------------

### Get convergence diagnostics using summarise_draws

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

Use `tidybayes::summarise_draws()` on grouped data frames to quickly obtain convergence diagnostics such as mean, median, sd, MAD, quantiles, Rhat, and effective sample sizes.

```R
m %>%
  spread_draws(condition_mean[condition]) %>%
  summarise_draws()
```

--------------------------------

### Basic Usage of compare_levels

Source: https://mjskay.github.io/tidybayes/reference/compare_levels.html

Demonstrates a basic application of compare_levels with default settings, using the RankCorr dataset.

```R
library(dplyr)
library(ggplot2)

data(RankCorr, package = "ggdist")

# Example usage (assuming RankCorr is structured appropriately):
# compare_levels(RankCorr, variable = corr, by = method) %>%
#   ggplot(aes(x = variable, y = value, color = by)) +
#   stat_halfeye()

```

--------------------------------

### Extracting posteriors

Source: https://mjskay.github.io/tidybayes/reference/index.html

Functions to get tidy draws or rvars of posterior distributions from objects, with helper functions for examining objects.

```APIDOC
## get_variables()

### Description
Get the names of the variables in a fitted Bayesian model.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## recover_types()

### Description
Decorate a model fit or sample with data types recovered from the input data.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## gather_draws() / spread_draws()

### Description
Extract draws of variables in a Bayesian model fit into a tidy data format.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## tidy_draws()

### Description
Get a sample of posterior draws from a model as a tibble.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## gather_emmeans_draws()

### Description
Extract a tidy data frame of draws of posterior distributions of "estimated marginal means" (emmeans/lsmeans) from a Bayesian model fit.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## ungather_draws() / unspread_draws()

### Description
Turn tidy data frames of variables from a Bayesian model back into untidy data.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## gather_rvars() / spread_rvars()

### Description
Extract draws from a Bayesian model into tidy data frames of random variables.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## nest_rvars() / unnest_rvars()

### Description
Nest and unnest `rvar` columns in data frames.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## summarise_draws(_<grouped_df>_)

### Description
Summaries of draws in `grouped_df` objects.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

--------------------------------

### Gather emmeans Pairwise Contrasts and Summarize

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

Perform pairwise comparisons using `emmeans::contrast()` and then convert the results to a tidy format with `gather_emmeans_draws()`. Summarize the contrasts using `median_qi()`.

```R
m_rst %>%
  emmeans::emmeans( ~ condition) %>% 
  emmeans::contrast(method = "pairwise") %>% 
  gather_emmeans_draws() %>% 
  median_qi()
```

--------------------------------

### Customize Index Variable Prefix

Source: https://mjskay.github.io/tidybayes/reference/compose_data.html

Customize the prefix for dimension index variables using the `.n_name` argument with `n_prefix()`. This example uses 'N' as the prefix.

```R
library(magrittr)

df = data.frame(
  plot = factor(paste0("p", rep(1:8, times = 2))),
  site = factor(paste0("s", rep(1:4, each = 2, times = 2)))
)

# you can use n_prefix() to define a different prefix (e.g. "N"):
df %>%
  compose_data(.n_name = n_prefix("N"))

```

--------------------------------

### Create a sample tidy dataset

Source: https://mjskay.github.io/tidybayes/articles/tidy-rstanarm.html

Generates a tibble named 'ABC' with 50 observations across five conditions, simulating a typical tidy data format for use in modeling.

```R
set.seed(5)
n = 10
n_condition = 5
ABC =
  tibble(
    condition = rep(c("A","B","C","D","E"), n),
    response = rnorm(n * 5, c(0,1,2,1,-1), 0.5)
  )
```

--------------------------------

### Get model variable names from rstanarm fit

Source: https://mjskay.github.io/tidybayes/articles/tidy-rstanarm.html

Retrieves a list of all variable names available for extraction from the fitted rstanarm model object 'm'.

```R
get_variables(m)
```

--------------------------------

### Add Predicted Probabilities (Matrix Format)

Source: https://mjskay.github.io/tidybayes/articles/tidy-posterior.html

Uses add_epred_rvars to get predictions from the ordinal model. The output for '.epred' is a matrix where columns represent probabilities for each category.

```r
tibble(mpg = c(21,22)) %>%
  add_epred_rvars(m_cyl)
```

--------------------------------

### Gather draws and summarize

Source: https://mjskay.github.io/tidybayes/reference/spread_draws.html

Demonstrates gathering draws for multiple parameters ('tau[i]', 'typical_r') into a long format using gather_draws, followed by summarizing them with median_qi to calculate the median and credible interval.

```r
RankCorr %>%
  gather_draws(tau[i], typical_r) %>%
  median_qi()
#> # A tibble: 4 × 8
#>       i .variable .value .lower .upper .width .point .interval
#>   <int> <chr>      <dbl>  <dbl>  <dbl>  <dbl> <chr>  <chr>
#> 1     1 tau        6.03   5.03   7.11    0.95 median qi       
#> 2     2 tau        3.30   2.41   4.46    0.95 median qi       
#> 3     3 tau        3.65   2.73   4.72    0.95 median qi       
#> 4    NA typical_r  0.548  0.309  0.778   0.95 median qi       
```

--------------------------------

### Plotting Posterior Predictive Intervals

Source: https://mjskay.github.io/tidybayes/articles/tidy-posterior.html

Use add_predicted_rvars() to get draws from the posterior predictive distribution and ggdist::stat_interval() to plot predictive bands alongside the data.

```r
ABC %>$
  data_grid(condition) %>$
  add_predicted_rvars(m) %>$
  ggplot(aes(y = condition)) + 
  stat_interval(aes(xdist = .prediction), .width = c(.50, .80, .95, .99)) + 
  geom_point(aes(x = response), data = ABC) + 
  scale_color_brewer()
```

--------------------------------

### Equivalent stat_lineribbon Implementation

Source: https://mjskay.github.io/tidybayes/index.html

This code block shows a manual implementation of stat_lineribbon using stat_summary for ribbons and lines, demonstrating how to plot median and quantile intervals.

```R
  stat_summary(
    aes(y = .prediction, fill = forcats::fct_rev(ordered(after_stat(.width))), group = -after_stat(.width)), 
    geom = "ribbon", point_interval = median_qi, fun.args = list(.width = c(.99, .95, .8, .5))
  ) +
  stat_summary(aes(y = .prediction), fun.y = median, geom = "line", color = "red", linewidth = 1.25)
```

--------------------------------

### Get convergence diagnostics for indexed variables

Source: https://mjskay.github.io/tidybayes/articles/tidy-rstanarm.html

Use summarise_draws to quickly obtain convergence diagnostics for indexed variables. This function is implemented for grouped data frames.

```r
m %>%
  spread_draws(b[,group]) %>%
  summarise_draws()
```

--------------------------------

### Extracting fits, predictions, and residuals

Source: https://mjskay.github.io/tidybayes/reference/index.html

Functions to get tidy draws or rvars from transformed linear predictors (“fits”), posterior predictions, or residuals.

```APIDOC
## add_epred_draws() / epred_draws()

### Description
Add draws from the posterior fit of a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_linpred_draws() / linpred_draws()

### Description
Add draws from the posterior linear predictor of a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_predicted_draws() / predicted_draws()

### Description
Add posterior predictive draws from a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_residual_draws() / residual_draws()

### Description
Add draws from the posterior residuals of a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_draws()

### Description
Add draws to a data frame in tidy format.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_epred_rvars() / epred_rvars()

### Description
Add `rvar`s for the posterior expectation of a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_linpred_rvars() / linpred_rvars()

### Description
Add `rvar`s for the posterior linear predictor of a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

```APIDOC
## add_predicted_rvars() / predicted_rvars()

### Description
Add `rvar`s for the posterior predictive of a model to a data frame.

### Parameters
(No parameters explicitly documented in the source)

### Request Example
(No request example provided in the source)

### Response
(No response details provided in the source)
```

--------------------------------

### data_list Function

Source: https://mjskay.github.io/tidybayes/reference/data_list.html

Creates a list with class `c("data_list", "list")`, similar to the base `list()` function.

```APIDOC
## data_list(...)

### Description
Creates a list with class `c("data_list", "list")` instead of `c("list")`, but largely otherwise acts like the `list()` function.

### Arguments
Additional arguments passed to `list()`.

### Value
An object of class `c("data_list", "list")`.
```

--------------------------------

### Load required R libraries

Source: https://mjskay.github.io/tidybayes/articles/tidy-brms.html

Loads all necessary libraries for data manipulation, visualization, and Bayesian modeling. Sets a custom tidybayes theme.

```r
library(magrittr)
library(dplyr)
library(purrr)
library(forcats)
library(tidyr)
library(modelr)
library(ggdist)
library(tidybayes)
library(ggplot2)
library(cowplot)
library(rstan)
library(brms)
library(ggrepel)
library(RColorBrewer)
library(gganimate)
library(posterior)
library(distributional)

theme_set(theme_tidybayes() + panel_border())
```

--------------------------------

### Basic usage of spread_rvars and gather_rvars

Source: https://mjskay.github.io/tidybayes/reference/spread_rvars.html

Demonstrates the basic syntax for extracting variables with specified dimensions using `spread_rvars` and `gather_rvars`.

```R
spread_rvars(model, a[i], b[i,v])
```

```R
gather_rvars(model, a[i], b[i,v])
```

--------------------------------

### Generate Nested Indices with x_at_y

Source: https://mjskay.github.io/tidybayes/reference/compose_data.html

Use `x_at_y()` within `compose_data` to generate nested indices, useful for models with hierarchical structures. This example creates a 'site' index specific to each 'plot'.

```R
library(magrittr)

df = data.frame(
  plot = factor(paste0("p", rep(1:8, times = 2))),
  site = factor(paste0("s", rep(1:4, each = 2, times = 2)))
)

# If you have nesting, you may want a nested index, which can be generated using x_at_y()
# Here, site[p] will give the site for plot p
df %>%
  compose_data(site = x_at_y(site, plot))

```

--------------------------------

### Display the first 10 rows of the sample dataset

Source: https://mjskay.github.io/tidybayes/articles/tidy-rstanarm.html

Prints the first 10 rows of the 'ABC' tibble to show its structure and sample data.

```R
head(ABC, 10)
```

--------------------------------

### Display ideal model summary

Source: https://mjskay.github.io/tidybayes/articles/tidybayes-residuals.html

Prints a summary of the fitted 'm_ideal' model, showing estimated coefficients, uncertainty, and convergence diagnostics.

```R
m_ideal
```

--------------------------------

### Visualize posterior predictions with posterior means

Source: https://mjskay.github.io/tidybayes/articles/tidybayes.html

Combine posterior predictions and posterior distributions of means for visualization. Use `spread_draws` to get draws, `mutate` for predictions, and `ggplot2` with `stat_interval` and `stat_pointinterval`.

```R
draws = m %>%
  spread_draws(condition_mean[condition], response_sd)

reps = draws %>%
  mutate(y_rep = rnorm(n(), condition_mean, response_sd))

ABC %>%
  ggplot(aes(y = condition)) + 
  stat_interval(aes(x = y_rep), .width = c(.95, .8, .5), data = reps) + 
  stat_pointinterval(aes(x = condition_mean), .width = c(.95, .66), position = position_nudge(y = -0.3), data = draws) + 
  geom_point(aes(x = response)) + 
  scale_color_brewer()
```

--------------------------------

### ggplot2 Density Plot with Customizations

Source: https://mjskay.github.io/tidybayes/reference/density_bins.html

Demonstrates creating a density plot using ggplot2 with custom aesthetics like shape, fill, and alpha. Includes warnings about dplyr version compatibility.

```r
geom_point(aes(x = hp, y = mpg, fill = ordered(cyl)), shape = 21, data = mtcars) +
  scale_alpha_continuous(range = c(0, 1)) +
  scale_fill_brewer(palette = "Set2")
#> Warning: Returning more (or less) than 1 row per `summarise()` group was deprecated in
#> dplyr 1.1.0.
#> ℹ Please use `reframe()` instead.
#> ℹ When switching from `summarise()` to `reframe()`, remember that `reframe()`
#>   always returns an ungrouped data frame and adjust accordingly.
```

--------------------------------

### Get model variables for ordinal regression

Source: https://mjskay.github.io/tidybayes/articles/tidy-rstanarm.html

Retrieves the names of all variables (coefficients and thresholds) from a fitted rstanarm ordinal regression model. Useful for understanding model structure and parameter names.

```R
get_variables(m_esoph_rs)
```

--------------------------------

### Plotting intervals with multiple probability levels

Source: https://mjskay.github.io/tidybayes/articles/tidy-brms.html

Demonstrates how to generate multiple probability intervals (e.g., 95%, 80%, 50%) using the `.width` argument in `median_qi()`. This facilitates comparing intervals of different widths.

```R
m %>%
  spread_draws(b_Intercept, r_condition[condition,]) %>%
  median_qi(condition_mean = b_Intercept + r_condition, .width = c(.95, .8, .5))
```

--------------------------------

### Mutate after spreading rvars

Source: https://mjskay.github.io/tidybayes/articles/tidy-posterior.html

After spreading rvars, use dplyr's mutate to perform calculations on the combined variables. This example calculates the mean within each condition by summing the intercept and condition effect.

```r
m %>
  spread_rvars(`b_Intercept`, r_condition[condition,Intercept]) %>
  mutate(condition_mean = b_Intercept + r_condition)
```

--------------------------------

### Summarize Posteriors with median_qi()

Source: https://mjskay.github.io/tidybayes/index.html

Use median_qi() from ggdist to obtain tidy output of point summaries and quantile intervals for posterior distributions. This function is part of the point_interval family.

```R
m %>%
  spread_draws(condition_mean[condition]) %>%
  median_qi(condition_mean)
```