priors {baggr} R Documentation

## Prior distributions in baggr

### Description

This page provides a list of all available distributions that can be used to specify priors in `baggr()`. These convenience functions are designed to allow the user to write the priors in the most "natural" way when implementing them in baggr. Apart from passing on the arguments, their only other role is to perform a rudimentary check if the distribution is specified correctly.

### Usage

```multinormal(location, Sigma)

lkj(shape, order = NULL)

normal(location, scale)

cauchy(location, scale)

uniform(lower, upper)
```

### Arguments

 `location` Mean for normal and multivariate normal (in which case `location` is a vector), and median for Cauchy distributions `Sigma` Variance-covariance matrix for multivariate normal. `shape` Shape parameter for LKJ `order` Order of LKJ matrix (typically it does not need to be specified, as it is inferred directly in the model) `scale` SD for Normal, scale for Cauchy `lower` Lower bound for Uniform `upper` Upper bound for Uniform

### Details

The prior choice in baggr is always done via 3 distinct arguments: `prior_hypermean`, `prior_hypersd`, and `prior_hypercor`.

These respectively refer to the priors on the average of the effects across the groups (hypermean), the standard deviation of the effects across the groups (hypersd), and the correlation in the distribution of parameters across groups when the model allows multivariate shrinkage (say on control group means and effects).

Notation for priors is "plain-text", in that you can write the distributions as `normal(5,10)`, `uniform(0,100)` etc. As with any other argument one has the option to simply input the prior directly, e.g. `prior_hypermean = normal(0,1)` , or by creating a named list of custom priors and then inputting the list to the argument `priors`. See the examples below for more.

Different parameters admit different priors:

• `prior_hypermean` will take `"normal"`, `"uniform"` and `"cauchy"` input for a scalar mean. For a vector mean, it will take any of these arguments and apply them independently to each component of the vector, or it can also take a `"multinormal"` argument (see the example below).

• `prior_hypersd` will take `"normal"` and `"uniform"`

• `prior_hypercor` allows `"lkj"` input

### Author(s)

Witold Wiecek, Rachael Meager

### References

Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. "Generating Random Correlation Matrices Based on Vines and Extended Onion Method." Journal of Multivariate Analysis 100, no. 9 (October 1, 2009): 1989-2001.

### Examples

```# (these are not the recommended priors -- for syntax illustration only)

# change the priors for 8 schools:
baggr(schools, model = "rubin", pooling = "partial",
prior_hypermean = normal(5,5),
prior_hypersd = normal(0,20))

# passing priors as a list
custom_priors <- list(hypercor = lkj(1), hypersd = normal(0,10),
hypermean = multinormal(c(0,0),matrix(c(10,3,3,10),2,2)))
microcredit_summary_data <- prepare_ma(microcredit, outcome = "consumption")
baggr(microcredit_summary_data, model = "mutau",
pooling = "partial", prior = custom_priors)

```

[Package baggr version 0.6.4 Index]