logit.zellner.prior {BoomSpikeSlab}  R Documentation 
A Zellnerstyle spike and slab prior for logistic regression models. See 'Details' for a definition.
LogitZellnerPrior( predictors, successes = NULL, trials = NULL, prior.success.probability = NULL, expected.model.size = 1, prior.information.weight = .01, diagonal.shrinkage = .5, optional.coefficient.estimate = NULL, max.flips = 1, prior.inclusion.probabilities = NULL)
predictors 
The design matrix for the regression problem. No missing data is allowed. 
successes 
The vector of responses, which can be 0/1,

trials 
A vector of the same length as successes, giving the
number of trials for each success count (trials cannot be less than
successes). If successes is binary (or 
prior.success.probability 
The overal prior guess at the
proportion of successes. This is used in two places. It is an
input into the intercept term of the default

expected.model.size 
A positive number less than 
prior.information.weight 
A positive scalar. Number of observations worth of weight that should be given to the prior estimate of beta. 
diagonal.shrinkage 
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. 
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). 
max.flips 
The maximum number of variable inclusion indicators the sampler will attempt to sample each iteration. If negative then all indicators will be sampled. 
prior.inclusion.probabilities 
A vector giving the prior
probability of inclusion for each variable. If 
A Zellnerstyle spike and slab prior for logistic regression. Denote the vector of coefficients by beta, and the vector of inclusion indicators by gamma. These are linked by the relationship beta[i] != 0 if gamma[i] = 1 and beta[i] == 0 if gamma[i] = 0. The prior is
beta  gamma ~ N(b, V),
gamma ~ Bernoulli(pi)
where pi is the vector of
prior.inclusion.probabilities
, and b is the
optional.coefficient.estimate
. Conditional on
gamma, the prior information matrix is
V^{1} = kappa * ((1  alpha) * x^Twx / n + alpha * diag(x^Twx/n))
The matrix x^Twx is, for suitable choice of the weight vector w, the total Fisher information available in the data. Dividing by n gives the average Fisher information in a single observation, multiplying by kappa then results in kappa units of "average" information. This matrix is averaged with its diagonal to ensure positive definiteness.
In the formula above, kappa is
prior.information.weight
, alpha is
diagonal.shrinkage
, and w is a diagonal matrix with all
elements set to prior.success.probability * (1 
prior.success.probability)
. The vector b and the matrix
V^{1} are both implicitly subscripted by gamma,
meaning that elements, rows, or columsn corresponding to gamma = 0
should be omitted.
Returns an object of class LogitZellnerPrior
, which is a list
with data elements encoding the selected prior values. It inherits
from LogitPrior
, which implies that it contains an element
prior.success.probability
.
This object is intended for use with logit.spike
.
Steven L. Scott
Hugh Chipman, Edward I. George, Robert E. McCulloch, M. Clyde, Dean P. Foster, Robert A. Stine (2001), "The Practical Implementation of Bayesian Model Selection" Lecture NotesMonograph Series, Vol. 38, pp. 65134. Institute of Mathematical Statistics.