Creates a spike and slab prior for use with lm.spike.
SpikeSlabPrior(x,
y = NULL,
expected.r2 = .5,
prior.df = .01,
expected.model.size = 1,
prior.information.weight = .01,
diagonal.shrinkage = .5,
optional.coefficient.estimate = NULL,
max.flips = -1,
mean.y = mean(y, na.rm = TRUE),
sdy = sd(as.numeric(y), na.rm = TRUE),
prior.inclusion.probabilities = NULL,
sigma.upper.limit = Inf)SpikeSlabPriorDirect(coefficient.mean,
coefficient.precision,
prior.inclusion.probabilities,
prior.df,
sigma.guess,
max.flips = -1,
sigma.upper.limit = Inf)
ConditionalZellnerPrior(xdim,
optional.coefficient.estimate = NULL,
expected.model.size = 1,
prior.information.weight = .01,
diagonal.shrinkage = .5,
max.flips = -1,
prior.inclusion.probabilities = NULL)
A list with with the components necessary to run lm.spike.
SpikeSlabPrior is intended for use in traditional regression
problems, when the matrix of predictors and the vector of responses
are available to the modeler.
ConditionalZellnerPrior is intended for cases where the
predictor variables are potentially unknown, because they depend on
model parameters or latent variables, for example. For models that
support ConditionalZellnerPrior, the underlying C++ code must know
where to find the relevant predictors on which to condition the prior.
The design matrix for the regression problem. Missing data is not allowed.
The vector of responses for the regression. Missing data is
not allowed. If y is not available, you can pass y =
NULL, and specify mean.y and sdy instead.
The expected R-square for the regression. The spike and slab prior
requires an inverse gamma prior on the residual variance of the
regression. The prior can be parameterized in terms of a guess at
the residual variance, and a "degrees of freedom" representing the
number of observations that the guess should weigh. The guess at
sigma^2 is set to (1-expected.r2) * var(y) .
A positive scalar representing the prior 'degrees of freedom' for
estimating the residual variance. This can be thought of as the
amount of weight (expressed as an observation count) given to the
expected.r2 argument.
A positive number less than ncol(x), representing a guess at
the number of significant predictor variables. Used to obtain the
'spike' portion of the spike and slab prior.
A positive scalar. Number of observations worth of weight that should be given to the prior estimate of beta.
The conditionally Gaussian prior for beta (the "slab") starts with a
precision matrix equal to the information in a single observation.
However, this matrix might not be full rank. The matrix can be made
full rank by averaging with its diagonal. diagonal.shrinkage
is the weight given to the diaonal in this average. Setting this to
zero gives Zellner's g-prior.
If desired, an estimate of the regression coefficients can be supplied. In most cases this will be a difficult parameter to specify. If omitted then a prior mean of zero will be used for all coordinates except the intercept, which will be set to mean(y).
The maximum number of variable inclusion indicators
the sampler will attempt to sample each iteration. If
max.flips <= 0 then all indicators will be sampled.
The mean of the response vector, for use in cases when specifying the response vector is undesirable.
The dimension of the predictor matrix.
The standard deviation of the response vector, for use in cases when specifying the response vector is undesirable.
A vector giving the prior probability of inclusion for each variable.
The largest acceptable value for the residual
standard deviation. A non-positive number is interpreted as
Inf.
The prior mean of the coefficients in the maximal model (with all variables included).
The prior precision (inverse variance) of the coefficients in the maximal model (with all variables included).
Prior estimate of the residual standard deviation.
Steven L. Scott
George and McCulloch (1997), "Approaches to Bayesian Variable Selection", Statistica Sinica, 7, 339 -- 373.
x <- cbind(1, matrix(rnorm(900), ncol = 9))
beta <- rep(0, 10)
beta[1] <- 3
beta[5] <- -4
beta[8] <- 2
y <- rnorm(100, x %*% beta)
## x has 10 columns, including the intercept
prior <- SpikeSlabPrior(x, y,
expected.model.size = 3, # expect 3 nonzero predictors
prior.df = .01, # weaker prior than the default
prior.information.weight = .01,
diagonal.shrinkage = 0, # use Zellner's prior
optional.coefficient.estimate = rep(0, 10) # shrink to zero
)
## now 'prior' can be fed to 'lm.spike'
model <- lm.spike(y ~ x - 1, niter = 1000, prior = prior)
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