eplogprob.marg calculates approximate marginal posterior inclusion
probabilities from p-values 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)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.
response variable
design matrix with a column of ones for the intercept
the value of the inclusion probability when if the p-value > 1/exp(1), where the lower bound approximation is not valid.
maximum value of the inclusion probability; used for the
bas.lm function to keep initial inclusion probabilities away from 1.
If the Intercept is included in the linear model, set the marginal inclusion probability corresponding to the intercept to 1
Merlise Clyde clyde@stat.duke.edu
Sellke, Bayarri and Berger (2001) provide a simple calibration of p-values
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 p-value 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 p-values are
obtained using statistics from the p simple linear regressions
P(F > (n-2) R2/(1 - R2)) where F ~ F(1, n-2) where R2 is the square of the correlation coefficient between y and X_j.
Sellke, Thomas, Bayarri, M. J., and Berger, James O. (2001), ``Calibration of p-values for testing precise null hypotheses'', The American Statistician, 55, 62-71.
bas
library(MASS)
data(UScrime)
UScrime[,-2] = log(UScrime[,-2])
eplogprob(lm(y ~ ., data=UScrime))
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