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

A model selection criterion proposed by Reiss et al. (2012), which employs cross-validation to estimate the overoptimism associated with the best candidate model of each size.

1 |

`y` |
outcome vector |

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

`nfold` |
number of "folds" (validation sets). The sample size must be divisible by this number. |

`pvec` |
vector of possible dimensions of the model to consider: by default, ranges from 1 (intercept only) to |

CVIC is similar to corrected AIC (Sugiura, 1978; Hurvich and Tsai, 1989), but instead of the nominal model dimension, it substitutes a measure of effective degrees of freedom (edf) that takes best-subset selection into account. The "raw" edf is obtained by cross-validation. Alternatively, one can refine the edf via constrained monotone smoothing, as described by Reiss et al. (2011).

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 |

`cv.pen` |
cross-validation penalty, as described by Reiss et al. (2011). |

`edf, edf.mon` |
effective degrees of freedom, before and after constrained monotone smoothing. |

`cvic` |
CVIC based on the raw edf. |

`cvic.mon` |
CVIC based on edf to which constrained monotone smoothing has been applied. |

`best, best.mon` |
vectors of logicals indicating which columns of the model matrix are included in the CVIC-minimizing model, without and with constrained monotone smoothing. |

Lei Huang huangracer@gmail.com and Philip Reiss phil.reiss@nyumc.org

Hurvich, C. M., and Tsai, C.-L. (1989). Regression and time series model selection in small samples. *Biometrika*, 76, 297–307.

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

Sugiura, N. (1978). Further analysis of the data by Akaike's information criterion and the finite corrections. *Communications in Statistics: Theory & Methods*, 7, 13–26.

`leaps`

in package leaps for best-subset selection; `pcls`

in package mgcv for the constrained monotone smoothing.

1 2 3 4 5 |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.