mombf: Moment and inverse moment Bayes factors for linear models.

In mombf: Model Selection with Bayesian Methods and Information Criteria

Moment and inverse moment Bayes factors for linear models.

Description

mombf computes moment Bayes factors to test whether a subset of regression coefficients are equal to some user-specified value. imombf computes inverse moment Bayes factors.

Usage

mombf(lm1, coef, g, prior.mode, baseDensity='normal', nu=3, theta0,
logbf=FALSE, B=10^5)
imombf(lm1, coef, g, prior.mode, nu = 1, theta0 , method='adapt',
nquant=100, B = 10^5)

Arguments

lm1	Linear model fit, as returned by lm1.
coef	Vector with indexes of coefficients to be tested. e.g. coef==c(2,3) and theta0==c(0,0) tests coef(lm1)[2]=coef(lm1)[3]=0.
g	Vector with prior parameter values. See dmom and dimom for details.
prior.mode	If specified, g is set such that the prior mode is prior.mode
baseDensity	Density upon which the Mom prior is based. baseDensity=='normal' results in the normal Mom prior, baseDensity=='t' in the t Mom prior with nu degrees of freedom.
nu	For mombf, nu specifies the degrees of freedom of the t Mom prior. It is ignored unless baseDensity=='t'. nu defaults to 3. For imombf, nu specifies the degrees of freedom for the inverse moment prior (see dimom for details). Defaults to nu=1, which Cauchy-like tails.
theta0	Null value for the regression coefficients. Defaults to 0.
logbf	If logbf==TRUE the natural logarithm of the Bayes factor is returned.
method	Numerical integration method to compute the bivariate integral (only used by imombf). For method=='adapt', the inner integral is evaluated (via integrate) at a series of nquant quantiles of the residual variance posterior distribution, 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. Only used if method=='adapt'.
B	Number of Monte Carlo samples to estimate the T Mom and the inverse moment Bayes factor. Only used in mombf if baseDensity=='t'. Only used in imombf if method=='MC'.

Details

These functions actually call momunknown and imomunknown, but they have a simpler interface. See dmom and dimom for details on the moment and inverse moment priors.

Value

mombf returns 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. imombf returns inverse moment Bayes factors.

Author(s)

David Rossell

References

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.

See Also

nlpMarginal for a better interface to integrated likelihoods and modelSelection to also search over the model space

Examples

##compute Bayes factor for Hald's data
data(hald)
lm1 <- lm(hald[,1] ~ hald[,2] + hald[,3] + hald[,4] + hald[,5])

# Set g so that interval (-0.2,0.2) has 5% prior probability
# (in standardized effect size scale)
priorp <- .05; q <- .2
gmom <- priorp2g(priorp=priorp,q=q,prior='normalMom')
gimom <- priorp2g(priorp=priorp,q=q,prior='iMom')

mombf(lm1,coef=2,g=gmom) #moment BF
imombf(lm1,coef=2,g=gimom,B=10^5) #inverse moment BF

mombf documentation built on Sept. 28, 2023, 5:06 p.m.