eplogprob.marg {BAS}  R Documentation 
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
eplogprob.marg(Y, X, thresh = 0.5, max = 0.99, int = TRUE)
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 
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.
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.
Merlise Clyde clyde@stat.duke.edu
Sellke, Thomas, Bayarri, M. J., and Berger, James O. (2001), “Calibration of pvalues for testing precise null hypotheses”, The American Statistician, 55, 6271.
library(MASS)
data(UScrime)
UScrime[,2] = log(UScrime[,2])
eplogprob(lm(y ~ ., data=UScrime))