logit.spike: Spike and slab logistic regression

In BoomSpikeSlab: MCMC for Spike and Slab Regression

Spike and slab logistic regression

Description

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

Usage

logit.spike(formula,
            niter,
            data,
            subset,
            prior = NULL,
            na.action = options("na.action"),
            contrasts = NULL,
            drop.unused.levels = TRUE,
            initial.value = NULL,
            ping = niter / 10,
            nthreads = 0,
            clt.threshold = 2,
            mh.chunk.size = 10,
            proposal.df = 3,
            sampler.weights = c("DA" = .333, "RWM" = .333, "TIM" = .333),
            seed = NULL,
            ...)

Arguments

formula	formula for the maximal model (with all variables included), this is parsed the same way as a call to glm, but no family argument is needed. Like glm, a two-column input format (success-count, failure-count). Otherwise, the response variable can be a logical or numeric vector. If numeric, then values >0 indicate a "success".
niter	The number of MCMC iterations to run. Be sure to include enough so you can throw away a burn-in set.
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 logit.spike' is called.
subset	An optional vector specifying a subset of observations to be used in the fitting process.
prior	A n object inheriting from SpikeSlabGlmPrior. If prior is supplied it will be used. Otherwise a prior distribution will constructed by calling LogitZellnerPrior.
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 logit.spike object. If a logit.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. There is some small overhead to stopping and starting threads. For small data sets, thread overhead will make it faster to run single threaded. For larger data sets multi-threading can speed things up substantially. This is all machine dependent, so please experiment.
clt.threshold	When the model is presented with binomial data (i.e. when the response is a two-column matrix) the data augmentation algorithm can be made more efficient by updating a single, asymptotically normal scalar quantity for each unique value of the predictors. The asymptotic result will be used whenever the number of successes or failures exceeds clt.threshold.
mh.chunk.size	The maximum number of coefficients to draw in a single "chunk" of a Metropolis-Hastings update. See details.
proposal.df	The degrees of freedom parameter to use in Metropolis-Hastings proposals. See details.
sampler.weights	The proportion of MCMC iterations spent in each of the three algorithms described in the Details section. This must be a vector of length 3, with names "DA", "RWM" and "TIM", containing non-negative elements that sum to (within numerical error .999 or 1.001 are okay).
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 passed to LogitZellnerPrior in the case where prior is NULL.

Details

Model parameters are updated using a composite of three Metropolis-Hastings updates. An auxiliary mixture sampling algorithm (Tuchler 2008) updates the entire parameter vector at once, but can mix slowly.

The second algorithm is a random walk Metropolis update based on a multivariate T proposal with proposal.df degrees of freedom. If proposal.df is nonpositive then a Gaussian proposal is used. The variance of the proposal distribution is based on the Fisher information matrix evaluated at the current draw of the coefficients.

The third algorithm is an independence Metropolis sampler centered on the posterior mode with variance determined by posterior information matrix (Fisher information plus prior information). If proposal.df > 0 then the tails of the proposal are inflated so that a multivariate T proposal is used instead.

For either of the two MH updates, at most mh.chunk.size coefficients will be updated at a time. At each iteration, one of the three algorithms is chosen at random. The auxiliary mixture sampler is the only one that can change the dimension of the coefficient vector. The MH algorithms only update the coefficients that are currently nonzero.

Value

Returns an object of class logit.spike, which inherits from lm.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

Tuchler (2008), "Bayesian Variable Selection for Logistic Models Using Auxiliary Mixture Sampling", Journal of Computational and Graphical Statistics, 17 76 – 94.

See Also

lm.spike SpikeSlabPrior, plot.logit.spike, PlotLogitSpikeFitSummary PlotLogitSpikeResiduals summary.logit.spike, predict.logit.spike.

Examples

if (requireNamespace("MASS")) {
  data(Pima.tr, package = "MASS")
  data(Pima.te, package = "MASS")
  pima <- rbind(Pima.tr, Pima.te)
  model <- logit.spike(type == "Yes" ~ ., data = pima, niter = 500)
  plot(model)
  plot(model, "fit")
  plot(model, "residuals")
  plot(model, "size")
  summary(model)
}

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