eplogprob calculates approximate marginal posterior inclusion
probabilities from p-values computed from a linear model using a lower bound
approximation to Bayes factors. Used to obtain initial inclusion
probabilities for sampling using Bayesian Adaptive Sampling bas.lm
eplogprob(lm.obj, thresh = 0.5, max = 0.99, int = TRUE)eplogprob 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. If the model
is not full rank, variables that are linearly dependent base on the QR
factorization will have NA for their p-values. In bas.lm, where the
probabilities are used for sampling, the inclusion probability is set to 0.
a linear model object
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.
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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