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.
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