reams (version 0.1)

eic: Extended (bootstrap) information criterion

Description

Model selection by an extended information criterion (EIC), based on nonparametric bootstrapping, was introduced by Ishiguro et al. (1997). This function implements the extension by Reiss et al. (2012) to adaptive linear model selection.

Usage

eic(y, X, nboot, pvec = 1:(ncol(X) + 1), say.which = FALSE, reuse = FALSE)

Arguments

y

outcome vector

X

model matrix. This should not include an intercept column; such a column is added by the function.

nboot

number of bootstrap samples.

pvec

vector of possible dimensions of the model to consider: by default, ranges from 1 (intercept only) to ncol(X) + 1 (full model).

say.which

logical: should the predictors selected for each bootstrap sample be reported?

reuse

logical: should the best full-data model of each size be reused in calculating the overoptimism estimate, as opposed to reselecting the best model of each size for each training set?

Value

A list with components

nlogsig2hat

value of the first (non-penalty) term of the criterion, i.e., sample size times log of MLE of the variance, for best model of each dimension in pvec.

penalty

the second (penalty) term of the criterion.

eic

the EIC, i.e., the sum of the previous two components.

best

a vector of logicals indicating which columns of the model matrix are included in the EIC-minimizing model.

Details

References

Ishiguro, M., Sakamoto, Y., and Kitagawa, G. (1997). Bootstrapping log likelihood and EIC, an extension of AIC. Annals of the Institute of Statistical Mathematics, 49, 411--434.

Reiss, P. T., Huang, L., Cavanaugh, J. E., and Roy, A. K. (2012). Resampling-based information criteria for adaptive linear model selection. Annals of the Institute of Statistical Mathematics, to appear. Available at http://works.bepress.com/phil_reiss/17

See Also

Examples

# Predicting fertility from provincial socioeconomic indicators
data(swiss)
eicobj <- eic(swiss$Fertility, swiss[ , -1], nboot=100)
eicobj$best