Define the type of tuning method used for regularization. Currently only used by tune.ahazpen
.
# Cross-validation
cv.control(nfolds=5, reps=1, foldid=NULL, trace=FALSE)# BIC-inspired
bic.control(factor = function(nobs){log(nobs)})
Number of folds for cross-validation. Default is
nfolds=5
. Each fold must
have size > 1, i.e. nfolds
must be
less than half the sample size.
Number of repetitions of cross-validation with
nfolds
folds. Default is rep=1
. A rep
larger than 1 can be useful to reduce variance of cross-validation
scores.
An optional vector of values between 1 and nfolds
identifying the fold to which each observation belongs. Supercedes
nfolds
and rep
if supplied.
Print progress of cross-validation. Default is trace=FALSE
.
Defines how strongly the number of nonzero penalty parameters penalizes the score in a BIC-type criterion; see the details.
An object with S3 class "ahaz.tune.control"
.
Type of penalty.
Function specified by factor
, if applicable
A function specifying how folds are calculated, if applicable.
How many repetitions of cross-validation, if applicable.
Print out progress?
For examples of usage, see tune.ahazpen
.
The regression coefficients of the semiparametric additive hazards model are estimated by solving a linear system of estimating equations of the form \(D\beta=d\) with respect to \(\beta\). The natural loss function for such a linear function is of the least-squares type $$L(\beta)=\beta' D \beta -2d'\beta.$$ This loss function is used for cross-validation as described by Martinussen & Scheike (2008).
Penalty parameter selection via a BIC-inspired approach was described by
Gorst-Rasmussen & Scheike (2011). With \(df\) is the degrees of freedom and \(n\) the number of
observations, we consider a BIC inspired criterion of the form
$$BIC = \kappa L(\beta) + df\cdot factor(n)$$
where \(\kappa\) is a scaling constant included to remove dependency on the
time scale and better mimick the behavior of a `real' (likelihood) BIC. The default factor=function(n){log(n)}
has
desirable theoretical properties but may be conservative in practice.
Gorst-Rasmussen, A. & Scheike, T. H. (2011). Independent screening for single-index hazard rate models with ultra-high dimensional features. Technical report R-2011-06, Department of Mathematical Sciences, Aalborg University.
Martinussen, T. & Scheike, T. H. (2008). Covariate selection for the semiparametric additive risk model. Scandinavian Journal of Statistics; 36:602-619.