The hatr function computes hat matrix (see Hastie and Tibshirani, 1990).
Usage
hatr(x, ...)
# S3 method for lmridge
hatr(x, ...)
Value
returns a list of matrix for each biasing parameter \(K\):
hatr
A list of hat matrix for each biasing parameter \(K\)
.
Arguments
x
An object of class "lmridge".
...
Not presently used in this implementation.
Author
Muhammad Imdad Ullah, Muhammad Aslam
Details
Hat matrix for scalar or vector values of biasing parameter provided as argument to lmridge. It is used to compute degrees of freedom for given \(K\), and error degree of freedom etc. The hat matrix can be computed using formula \(X(X'X+kI)^{-1}X'\) equivalently \(\sum{\frac{\lambda_j}{(\lambda_j+k)}}\).
References
Cule, E. and De lorio, M. (2012). A semi-Automatic method to guide the choice of ridge parameter in ridge regression. arXiv:abs/1205.0686v1 [stat.AP].
Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall.
Imdad, M. U. Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan), 2017.
See Also
The ridge model fitting lmridge, ridge Var-Cov matrix vcov.lmridge
mod <- lmridge(y~., as.data.frame(Hald), K = c(0, 0.1, 0.2, 0.3))
## Hat matrix for each biasing parameterhatr(mod)
## Hat matrix for first biasing parameter i.e. K = 0.1hatr(mod)[[2]]