| momknown {mombf} | R Documentation |
momknown and momunknown compute moment Bayes
factors for linear models when sigma^2 is known and unknown,
respectively. The functions can also be used to compute approximate
Bayes factors for generalized linear models and other settings.
imomknown, imomunknown compute inverse
moment Bayes factors. zbfknown,
zbfunknown compute Bayes factors based on the
Zellner-Siow g-prior.
momknown(theta1hat, V1, n, g = 1, theta0, sigma, logbf = FALSE) momunknown(theta1hat, V1, n, nuisance.theta, g = 1, theta0, ssr, logbf = FALSE) imomknown(theta1hat, V1, n, nuisance.theta, g = 1, nu = 1, theta0, sigma, method='adapt', B=10^5) imomunknown(theta1hat, V1, n, nuisance.theta, g = 1, nu = 1, theta0, ssr, method='adapt', nquant = 100, B = 10^5) zbfknown(theta1hat, V1, n, g = 1, theta0, sigma, logbf = FALSE) zbfunknown(theta1hat, V1, n, nuisance.theta, g = 1, theta0, ssr, logbf = FALSE)
theta1hat |
Vector with regression coefficients estimates. |
V1 |
Matrix proportional to the covariance of
theta1hat. For linear models, the covariance is sigma^2*V1. |
n |
Sample size. |
nuisance.theta |
Number of nuisance regression coefficients, i.e. coefficients that we do not wish to test for. |
ssr |
Sum of squared residuals from a linear model call. |
g |
Prior parameter. See dmom and dimom for details. |
theta0 |
Null value for the regression coefficients. Defaults to 0. |
sigma |
Dispersion parameter is sigma^2. |
logbf |
If logbf==TRUE the natural logarithm of the Bayes
factor is returned. |
nu |
Prior parameter for the inverse moment prior. See
dimom for details. Defaults to nu=1, which Cauchy-like
tails. |
method |
Numerical integration method (only used by
imomknown and imomunknown).
Set method=='adapt' in imomknown to integrate using adaptive
quadrature of functions as implemented in the function
integrate. In imomunknown the integral is evaluated as in
imomknown at a series of
nquant quantiles of the posterior for sigma, and then
averaged as described in Johnson (1992).
Set method=='MC' to use Monte Carlo integration. |
nquant |
Number of quantiles at which to evaluate the integral
for known sigma. |
B |
Number of Monte Carlo samples to estimate the inverse moment
Bayes factor. Ignored if method!='MC'. |
See dmom and dimom for details on the moment and inverse
moment priors.
The Zellner-Siow g-prior is given by dmvnorm(theta,theta0,n*g*V1).
momknown and momunknown return the moment Bayes factor to compare the model where
theta!=theta0
with the null model where theta==theta0. Large values favor the
alternative model; small values favor the null.
imomknown and imomunknown return
inverse moment Bayes factors.
zbfknown and zbfunknown return Bayes factors based on the Zellner-Siow g-prior.
David Rossell
See http://rosselldavid.googlepages.com for technical reports.
For details on the quantile integration, see Johnson, V.E. A Technique for Estimating Marginal Posterior Densities in Hierarchical Models Using Mixtures of Conditional Densities. Journal of the American Statistical Association, Vol. 87, No. 419. (Sep., 1992), pp. 852-860.
mombf and
imombf for a simpler interface to compute Bayes
factors in linear regression. mode2g for prior elicitation.
#simulate data from probit regression set.seed(4*2*2008) n <- 50; theta <- c(log(2),0) x <- matrix(NA,nrow=n,ncol=2) x[,1] <- rnorm(n,0,1); x[,2] <- rnorm(n,.5*x[,1],1) p <- pnorm(x[,1]*theta[1]+x[,2]+theta[2]) y <- rbinom(n,1,p) #fit model glm1 <- glm(y~x[,1]+x[,2],family=binomial(link = "probit")) thetahat <- coef(glm1) V <- summary(glm1)$cov.scaled #compute Bayes factors to test whether x[,1] can be dropped from the model g <- .5 bfmom.1 <- momknown(thetahat[2],V[2,2],n=n,g=g,sigma=1) bfimom.1 <- imomknown(thetahat[2],V[2,2],n=n,nuisance.theta=2,g=g,sigma=1) bfmom.1 bfimom.1