mombf (version 3.1.3)

getBIC: Obtain BIC and EBIC

Description

Obtain Bayesian Information Criterion and Extended Bayesian Information Criterion

Usage

getBIC(object)
  getEBIC(object)

Value

BIC or EBIC values for all models enumerated / visited by modelSelection

Arguments

object

Object of class msfit returned by modelSelection

Author

David Rossell

Details

Let p be the total number of parameters and n the sample size. The BIC of a model k with p_k parameters is

- 2 L_k + p_k log(n)

and the EBIC is

- 2 L_k + p_k log(n) + 2 log(p choose p_k)

Function modelSelection returns the log posterior probability of a model, postProb = log(m_k) + log(prior k), where m_k is the marginal likelihood of the model and prior k its prior probability.

When running function modelSelection with priorCoef=bicprior() and priorDelta=modelunifprior(), the BIC approximation is used for m_k, that is

log(m_k) = L_k - 0.5 * p_k log(n)

and all models are equally likely a priori, log(prior k)= p log(1/2). Then the BIC can be easily recovered

BIC_k= -2 * [postProb + p log(2)]

When using priorCoef=bicprior() and priorDelta=modelbbprior(), log(prior k)= - log(p+1) - log(p choose p_k), hence

EBIC_k= -2 * [postProb + log(p+1)].

See Also

modelSelection to perform model selection

Examples

x <- matrix(rnorm(100*3),nrow=100,ncol=3)
theta <- matrix(c(1,1,0),ncol=1)
y <- x %*% theta + rnorm(100)
ybin <- y>0

#Obtain BIC
ms= modelSelection(ybin, x=x, priorCoef=bicprior(),
priorDelta=modelunifprior(), family='binomial')
getBIC(ms)

#Obtain EBIC
ms2= modelSelection(ybin, x=x, priorCoef=bicprior(),
priorDelta=modelbbprior(), family='binomial')
getEBIC(ms2)