independent.spike.slab.prior {BoomSpikeSlab}  R Documentation 
A spike and slab prior assuming a priori independence.
Description
A spike and slab prior on the regression coefficients. The prior distribution assumes coefficients to be independent.
Usage
IndependentSpikeSlabPrior(x = NULL,
y = NULL,
expected.r2 = .5,
prior.df = .01,
expected.model.size = 1,
prior.beta.sd = NULL,
optional.coefficient.estimate = NULL,
mean.y = mean(y, na.rm = TRUE),
sdy = sd(as.numeric(y), na.rm = TRUE),
sdx = apply(as.matrix(x), 2, sd, na.rm = TRUE),
prior.inclusion.probabilities = NULL,
number.of.observations = nrow(x),
number.of.variables = ncol(x),
scale.by.residual.variance = FALSE,
sigma.upper.limit = Inf)
Arguments
x 
The design matrix for the regression problem. Missing data is not allowed. 
y 
The vector of responses for the regression. Missing data is not allowed. 
expected.r2 
The expected Rsquare 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 
prior.df 
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.model.size 
A positive number less than 
prior.beta.sd 
A vector of positive numbers giving the prior standard deviation of each model coefficient, conditionl on inclusion. If NULL it will be set to 10 * the ratio of sdy / sdx. 
optional.coefficient.estimate 
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). 
mean.y 
The mean of the response vector, for use in cases when specifying the response vector is undesirable. 
sdy 
The standard deviation of the response vector, for use in cases when specifying the response vector is undesirable. 
sdx 
The standard deviations to use when scaling the prior sd of each coefficient. 
prior.inclusion.probabilities 
A vector giving the prior probability of inclusion for each variable. 
number.of.observations 
The number of observations in the data to be modeled. 
number.of.variables 
The number of potential predictor variables in the data to be modeled. 
scale.by.residual.variance 
If 
sigma.upper.limit 
The largest acceptable value for the residual
standard deviation. A nonpositive number is interpreted as

Value
A list with with the components necessary to run lm.spike
with
method "DA".
Author(s)
Steven L. Scott
References
Ghosh and Clyde (2011) "RaoBlackwellization for Bayesian variable selection and model averaging in linear and binary regression: A novel data augmentation approach", Journal of the American Statistical Association, 106 10411052. https://homepage.stat.uiowa.edu/~jghsh/ghosh_clyde_2011_jasa.pdf
Examples
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 < IndependentSpikeSlabPrior(x, y,
expected.model.size = 3, # expect 3 nonzero predictors
prior.df = .01, # weaker prior than the default
optional.coefficient.estimate = rep(0, 10) # shrink to zero
)
## now 'prior' can be fed to 'lm.spike'
x < x[, 1]
model < lm.spike(y ~ x, niter = 1000, prior = prior, model.options = OdaOptions())