momknown: Bayes factors for moment, inverse moment and Zellner-Siow...
In mombf: Bayesian Model Selection and Averaging for Non-Local and Local Priors

Description Usage Arguments Details Value Author(s) References See Also Examples

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

#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