mombf (version 3.3.0)

bestBIC: Model with best AIC, BIC, EBIC or other general information criteria (getIC)

Description

Search for the regression model attaining the best value of the specified information criterion

Usage

bestAIC(...)
  bestBIC(...)
  bestEBIC(...)
  bestIC(..., penalty)

Value

data.frame with the requested information criterion for all models (when enumeration is feasible) or those visited by an MCMC model search in modelSelection (when enumeration is not feasible)

Arguments

...

Arguments passed on to modelSelection. The first and main argument is a model formula, see the examples

penalty

General information penalty. For example, since the AIC penalty is 2, bestIC(...,penalty=2) is the same as bestAIC(...)

Author

David Rossell

Details

For details on the information criteria see help(getBIC).

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

#BIC for all models (the intercept is also selected in/out)
bestBIC(y ~ x[,1] + x[,2])

#Same, but setting the BIC's log(n) penalty manually
#change the penalty for other General Info Criteria
n= nrow(x)
bestIC(y ~ x[,1] + x[,2], penalty=log(n))