eplogprob.marg {BAS}R Documentation

eplogprob.marg - Compute approximate marginal inclusion probabilities from pvalues


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)



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


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.


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 p-values for testing precise null hypotheses”, The American Statistician, 55, 62-71.

See Also



UScrime[,-2] = log(UScrime[,-2])
eplogprob(lm(y ~ ., data=UScrime))

[Package BAS version 1.7.1 Index]