mombf: Moment and inverse moment Bayes factors for linear models.
In mombf: Bayesian Model Selection and Averaging for Non-Local and Local Priors

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

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. zellnerbf computes Bayes factors based on the Zellner-Siow prior (used to build the moment prior).

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)

`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'`.

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. The Zellner-Siow g-prior is given by dmvnorm(theta,theta0,n*g*V1).

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. zellnerbf returns 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.

momunknown, imomunknown and zbfunknown for another interface to compute Bayes factors. momknown, imomknown and zbfknown to compute Bayes factors assuming that the dispersion parameter is known, and for approximate Bayes factors for GLMs

##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
zellnerbf(lm1,coef=2,g=1) #BF based on Zellner's g-prior