priors function

Prior distributions in baggr

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.

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.)

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)

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.

Author(s)

Witold Wiecek, Rachael Meager