poisson.spike: Spike and slab Poisson regression

In BoomSpikeSlab: MCMC for Spike and Slab Regression

Spike and slab Poisson regression

Description

MCMC algorithm for Poisson regression models with a 'spike-and-slab' prior that places some amount of posterior probability at zero for a subset of the coefficients.

Usage

poisson.spike(formula,
              exposure = 1,
              niter,
              data,
              subset,
              prior = NULL,
              na.action = options("na.action"),
              contrasts = NULL,
              drop.unused.levels = TRUE,
              initial.value = NULL,
              ping = niter / 10,
              nthreads = 4,
              seed = NULL,
              ...)

Arguments

formula	A model formula, as would be passed to glm, specifying the maximal model (i.e. the model with all predictors included).
exposure	A vector of exposure durations matching the length of the response vector. If exposure is of length 1 it will be recycled.
niter	The number of MCMC iterations to run.
data	An optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which poisson.spike is called.
subset	An optional vector specifying a subset of observations to be used in the fitting process.
prior	A list such as that returned by SpikeSlabPrior. If prior is supplied it will be used. Otherwise a prior distribution will be built using the remaining arguments. See SpikeSlabPrior.
na.action	A function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The factory-fresh default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.
contrasts	An optional list. See the contrasts.arg of model.matrix.default.
drop.unused.levels	A logical value indicating whether factor levels that are unobserved should be dropped from the model.
initial.value	Initial value for the MCMC algorithm. Can either be a numeric vector, a glm object (from which the coefficients will be used), or a poisson.spike object. If a poisson.spike object is supplied, it is assumed to be from a previous MCMC run for which niter additional draws are desired. If a glm object is supplied then its coefficients will be used as the initial values for the simulation.
ping	If positive, then print a status update to the console every ping MCMC iterations.
nthreads	The number of CPU-threads to use for data augmentation.
seed	Seed to use for the C++ random number generator. It should be NULL or an int. If NULL the seed value will be taken from the global .Random.seed object.
...	Extra arguments to be passed to SpikeSlabPrior.

Details

The MCMC algorithm used here is based on the auxiliary mixture sampling algorithm published by Fruhwirth-Schnatter, Fruhwirth, Held, and Rue (2009).

Value

Returns an object of class poisson.spike. The returned object is a list with the following elements.

beta	A niter by ncol(x) matrix of regression coefficients, many of which may be zero. Each row corresponds to an MCMC iteration.
prior	The prior used to fit the model. If a prior was supplied as an argument it will be returned. Otherwise this will be the automatically generated prior based on the other function arguments.

Author(s)

Steven L. Scott

References

Sylvia Fruhwirth-Schnatter, Rudolf Fruhwirth, Leonhard Held, and Havard Rue. Statistics and Computing, Volume 19 Issue 4, Pages 479-492. December 2009

See Also

lm.spike SpikeSlabPrior, plot.lm.spike, summary.lm.spike, predict.lm.spike.

Examples

simulate.poisson.spike <- function(n = 100, p = 10, ngood = 3, niter=1000){
  x <- cbind(1, matrix(rnorm(n * (p-1)), nrow=n))
  beta <- c(rnorm(ngood), rep(0, p - ngood))
  lambda <- exp(x %*% beta)
  y <- rpois(n, lambda)
  x <- x[,-1]
  model <- poisson.spike(y ~ x, niter=niter)
  return(invisible(model))
}
model <- simulate.poisson.spike()
plot(model)
summary(model)

BoomSpikeSlab documentation built on May 29, 2024, 5:07 a.m.