mombf (version 3.5.4)

getBIC: Obtain AIC, BIC, EBIC or other general information criteria (getIC)

Description

Extract information criteria from an msfit object.

Usage

getAIC(object)
  getBIC(object)
  getEBIC(object)
  getIC(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)

the AIC is

- 2 L_k + p_k 2

the EBIC is

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

and a general information criterion with a given model size penalty

- 2 L_k + p_k penalty

For getBIC() to work, object must be the result returned by modelSelection setting priorCoef=bic() and priorDelta=modelunifprior()

For getEBIC() it is priorCoef=bic() and priorDelta=modelbbprior()

For getAIC() it is priorCoef=aic() and priorDelta=modelunifprior()

For getIC() it is priorCoef=ic() and priorDelta=modelunifprior()

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)