eplogprob.marg {BAS}  R Documentation 
eplogprob.marg  Compute approximate marginal inclusion probabilities from pvalues
Description
eplogprob.marg
calculates approximate marginal posterior inclusion
probabilities from pvalues computed from a series of simple linear
regression models using a lower bound approximation to Bayes factors. Used
to order variables and if appropriate obtain initial inclusion probabilities
for sampling using Bayesian Adaptive Sampling bas.lm
Usage
eplogprob.marg(Y, X, thresh = 0.5, max = 0.99, int = TRUE)
Arguments
Y 
response variable 
X 
design matrix with a column of ones for the intercept 
thresh 
the value of the inclusion probability when if the pvalue > 1/exp(1), where the lower bound approximation is not valid. 
max 
maximum value of the inclusion probability; used for the

int 
If the Intercept is included in the linear model, set the marginal inclusion probability corresponding to the intercept to 1 
Details
Sellke, Bayarri and Berger (2001) provide a simple calibration of pvalues
BF(p) = e p log(p)
which provide a lower bound to a Bayes factor for comparing H0: beta = 0 versus H1: beta not equal to 0, when the pvalue p is less than 1/e. Using equal prior odds on the hypotheses H0 and H1, the approximate marginal posterior inclusion probability
p(beta != 0  data ) = 1/(1 + BF(p))
When p > 1/e, we set the marginal inclusion probability to 0.5 or the value
given by thresh
. For the eplogprob.marg the marginal pvalues are
obtained using statistics from the p simple linear regressions
P(F > (n2) R2/(1  R2)) where F ~ F(1, n2) where R2 is the square of the correlation coefficient between y and X_j.
Value
eplogprob.prob
returns a vector of marginal posterior
inclusion probabilities for each of the variables in the linear model. If
int = TRUE, then the inclusion probability for the intercept is set to 1.
Author(s)
Merlise Clyde clyde@stat.duke.edu
References
Sellke, Thomas, Bayarri, M. J., and Berger, James O. (2001), “Calibration of pvalues for testing precise null hypotheses”, The American Statistician, 55, 6271.
See Also
Examples
library(MASS)
data(UScrime)
UScrime[,2] = log(UScrime[,2])
eplogprob(lm(y ~ ., data=UScrime))