genRidgePenaltyMat {porridge} | R Documentation |
Penalty parameter matrix for generalized ridge regression.
Description
The function produces an unscaled penalty parameter matrix to be used in the generalized ridge regression estimator.
Usage
genRidgePenaltyMat(pr, pc=pr, type="2dimA")
Arguments
pr |
A positive |
pc |
A positive |
type |
A |
Details
Various ridge penalty matrices are implemented.
The type="common"
-option supports the ‘homogeneity’ ridge penalization proposed by Anatolyev (2020). The ridge penalty matrix for a
-dimensional regression parameter
is such that:
This penalty matrix encourages shrinkage of the elements of to a common effect value.
The type="fused1dim"
-option facilitates the 1-dimensional fused ridge estimation of Goeman (2008). The ridge penalty matrix for a
-dimensional regression parameter
is such that:
This penalty matrix aims to shrink contiguous (as defined by their index) elements of towards each other.
The type="fused2dimA"
- and type="fused2dimD"
-options facilitate 2-dimensional ridge estimation as proposed by Lettink et al. (2022). It assumes the regression parameter is endowed with a 2-dimensional layout. The columns of this layout have been stacked to form . The 2-dimensional fused ridge estimation shrinks elements of
that are neighbors in the 2-dimensional layout towards each other. The two options use different notions of neighbors. If
type="fused2dimA"
, the ridge penalty matrix for a
-dimensional regression parameter
is such that:
where and
are the row and column dimension, respectively, of the 2-dimensional layout. This penalty matrix intends to shrink the elements of
along the axes of the 2-dimensional layout. If
type="fused2dimD"
, the ridge penalty matrix for a
-dimensional regression parameter
is such that:
This penalty matrix shrinks the elements of along the diagonally to the axes of the 2-dimensional layout. The penalty matrices
generated by
type="fused2dimA"
- and type="fused2dimD"
-options may be combined.
Value
The function returns a non-negative definite matrix
.
Author(s)
W.N. van Wieringen.
References
Anatolyev, S. (2020), "A ridge to homogeneity for linear models", Journal of Statistical Computation and Simulation, 90(13), 2455-2472.
Goeman, J.J. (2008), "Autocorrelated logistic ridge regression for prediction based on proteomics spectra", Statistical Applications in Genetics and Molecular Biology, 7(2).
Lettink, A, Chinapaw, M.J.M., van Wieringen, W.N. (2022), "Two-dimensional fused targeted ridge regression for health indicator prediction from accelerometer data", submitted.
See Also
ridgeGLM
Examples
# generate unscaled general penalty parameter matrix
Dfused <- genRidgePenaltyMat(10, type="fused1dim")