hatl: Liu Regression: Hat Matrix
In liureg: Liu Regression with Liu Biasing Parameters and Statistics

Description Usage Arguments Details Value Note Author(s) References See Also Examples

The hatl function computes hat matrix of Liu regression (Liu (1993) <doi:10.1080/03610929308831027>).

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hatl(object, ...)
## S3 method for class 'liu'
hatl(object, ...)

`object`	An object of class "liu".
`...`	Not presently used in this implementation.

Hat matrix for scalar or vector values of biasing parameter d provided as argument to liu function. It is used to compute degrees of freedom for given d, and error degree of freedom etc. The hat matrix can be computed using formula X(X'X+I_p)^{-1}(X'X+dI_p)(X'X)^{-1}X'.

Returns a list of matrix for each biasing parameter d:

hatl

A list of hat matrix for each biasing parameter d.

The hat matrix is not idempotent because it is not projection matrix, therefore it is called quasi-projection matrix.

Muhammad Imdad Ullah, Muhammad Aslam

Imdad, M. U. (2017). Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan).

Imdadullah, M., Aslam, M., and Altaf, S. (2017). liureg: A comprehensive R Package for the Liu Estimation of Linear Regression Model with Collinear Regressors. The R Journal, 9 (2), 232–247.

Liu, K. (1993). A new Class of Biased Estimate in Linear Regression. Journal of Statistical Planning and Inference, 141, 189–196. http://doi.org/10.1080/03610929308831027.

Liu model fitting liu, Liu residuals residuals.liu, Liu PRESS press.liu, Testing of Liu Coefficients summary.liu

mod<-liu(y ~ . , data = as.data.frame(Hald), d = c(-5, -1, 0.2, 0.3))
## Hat matrix for each biasing parameter
hatl(mod)

## Hat matrix for second biasing parameter i.e. d = -1
hatl(mod)[[2]]

## Diagonal element of hat matrix for second biasing parameter
diag(hatl(mod)[[2]])