priors: Prior distributions in baggr

In baggr: Bayesian Aggregate Treatment Effects

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)

lognormal(mu, sigma)

student_t(nu, mu, sigma)

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
mu	mean of ln(X) for lognormal or location for Student's generalised T
sigma	SD of ln(X) for lognormal or scale for Student's generalised T
nu	degrees of freedom for Student's generalised T
lower	Lower bound for Uniform
upper	Upper bound for Uniform

Details

The prior choice in baggr is done via distinct arguments for each type of prior, e.g. prior_hypermean, or a named list of several passed to prior. See the examples below.

Notation for priors is "plain-text", in that you can write the distributions as normal(5,10), uniform(0,100) etc.

Different parameters admit different priors (see baggr for explanations of what the different prior_ arguments do):

• prior_hypermean, prior_control, and prior_beta will take "normal", "uniform", "lognormal", and "cauchy" input for scalars. For a vector hypermean (see "mutau" model), 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, prior_control_sd, and prior_sigma will take "normal", "uniform", and "lognormal" but negative parts of the distribution are truncated

• prior_hypercor allows "lkj" input (see Lewandowski et al.)

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)

baggr documentation built on March 31, 2023, 10:02 p.m.