mcmcsae-family: Functions for specifying a sampling distribution and link...

In mcmcsae: Markov Chain Monte Carlo Small Area Estimation

Functions for specifying a sampling distribution and link function

Description

These functions are intended for use in the family argument of create_sampler. In future versions these functions may gain additional arguments, but currently the corresponding functions gaussian and binomial can be used as well.

Usage

f_gamma(
  link = "log",
  shape.vec = ~1,
  shape.prior = pr_gamma(0.1, 0.1),
  control = set_MH(type = "RWLN", scale = 0.2, adaptive = TRUE)
)

f_gaussian_gamma(link = "identity", var.data, ...)

f_poisson(link = "log", size = 100)

f_gaussian(link = "identity")

f_binomial(link = c("logit", "probit"))

f_negbinomial(link = "logit")

f_multinomial(link = "logit", K = NULL)

Arguments

link	the name of a link function. Currently the only allowed link functions are: "identity" for (log-)Gaussian sampling distributions, "logit" (default) and "probit" for binomial distributions and "log" for negative binomial sampling distributions.
shape.vec	optional formula specification of unequal shape parameter for gamma family
shape.prior	prior for gamma shape parameter. Supported prior distributions: pr_fixed with a default value of 1, pr_exp and pr_gamma. The current default is pr_gamma(shape=0.1, rate=0.1).
control	options for the Metropolis-Hastings algorithm employed in case the shape parameter is to be inferred. Function set_MH can be used to change the default options. The two choices of proposal distribution type supported are "RWLN" for a random walk proposal on the log-shape scale, and "gamma" for an approximating gamma proposal, found using an iterative algorithm. In the latter case, a Metropolis-Hastings accept-reject step is currently omitted, so the sampling algorithm is an approximate one, though often quite accurate and efficient.
var.data	the (variance) data for the gamma part of family gaussian_gamma.
...	further arguments passed to f_gamma.
size	size or dispersion parameter of the negative binomial distribution used internally to approximate the Poisson distribution. This should be set to a relatively large value (default is 100), corresponding to negligible overdispersion, to obtain a good approximation. However, too large values may cause slow MCMC exploration of the posterior distribution.
K	number of categories for multinomial model; this must be specified for prior predictive sampling.

Value

A family object.

References

J.W. Miller (2019). Fast and Accurate Approximation of the Full Conditional for Gamma Shape Parameters. Journal of Computational and Graphical Statistics 28(2), 476-480.

mcmcsae documentation built on April 12, 2025, 2:25 a.m.