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