Estimation of the ridge parameter

Maximum likelihood estimation of the ridge parameter by cross-validation

Usage

ridgeParamEst(dat, X, weights = rep(1,times=nRows), refs, 
  tol=1.0e-010, only.ridge=FALSE,  doPlot=FALSE,
  col="blue",type="l", ...)

Arguments

dat: the data matrix.
X: the design matrix.
weights: weights on the cases of the design matrix.
refs: a vector specifying validation group membership. Default is to construct refs using a method that is a function of the sample size N: if N<=20, leave-one-out is used refs=1:N, if N<=40, 10-fold Cross Validation is used where group membership is chosen randomly but with equal size groups, otherwise 5-fold CV with random group memberships.
tol: the sensitivity in calculations near zero.
only.ridge: logical, whether only the ridge Parameters should be passed back or additionally the Cross Validation penalised likelihood.
doPlot: logical, whether a plot of -2logL vs a candidate for the ridge parameter should be drawn.
col: color of Plot symbols.
type: type of Plot symbols.
...: further plot arguments.

Details

This function estimates the ridge parameter when applying ridge regularization to a sample correlation matrix of residuals. The ridge parameter is estimated to maximize the normal likelihood as estimated via cross validation (Warton 2008).

Value

A list with the following component:

ridgeParameter: the estimated ridge parameter

If only.ridge=FALSE the returned list additionally contains the element:

minLL: the minimum of the negative log-likelihood

References

Warton D.I. (2008). Penalized normal likelihood and ridge regularization of correlation and covariance matrices. Journal of the American Statistical Association 103, 340-349.

Author

David Warton <David.Warton@unsw.edu.au> and Ulrike Naumann.

Examples

data(spider)
spiddat <- mvabund(spider$abund)
X <- as.matrix(spider$x)

ridgeParamEst(dat = spiddat, X = model.matrix(spiddat~X))
#> $ridgeParameter
#> [1] 0.1897086
#> 
#> $minLL
#> [1] 2163.444
#>