View source: R/summary.lmridge.R
summary.lmridge | R Documentation |
The summary
method for class "lmridge" for scalar or vector biasing parameter K (Cule and De lorio, 2012).
## S3 method for class 'lmridge' summary(object, ...) ## S3 method for class 'summary.lmridge' print(x, digits = max(3, getOption("digits") - 3), signif.stars = getOption("show.signif.stars"), ...)
object |
An "lmridge" object, typically generated by a call to |
x |
An object of class |
signif.stars |
logical: if |
digits |
The number of significant digits to use when printing. |
... |
Not presently used in this implementation. |
print.summary.lmridge
tries to be smart about formatting the coefficients, standard errors etc. and additionally gives 'significance stars' if signif.stars
is TRUE
.
The function summary
computes and returns a list of summary statistics of the fitted linear ridge regression model for scalar or vector value biasing parameter K given as argument in lmridge
function. All summary information can be called using list object summaries
.
coefficients |
A p * 5 matrix with columns for the scaled estimated, descaled estimated coefficients, scaled standard error, scaled t-statistics, and corresponding p-value (two-tailed). The Intercept term is computed by the relation \hat{β}_{R0K}=ybar-∑_{j=1}^p(Xbar_j \hat{β}_{R0K}). The standard error of intercept term is computed as, SE(\hat{β}_{R_{0K}})=√{Var(ybar)+Xbar_j^2 diag[Cov(\hat{β}_{R})]}. |
stats |
Ridge related statistics of R-squared, adjusted R-squared, F-statistics for testing of coefficients, AIC and BIC values for given biasing parameter K. |
rmse1 |
Minimum MSE value for given biasing parameter K. |
rmse2 |
Value of K at which MSE is minimum. |
K |
Value of given biasing parameter. |
df1 |
Numerator degrees of freedom for p-value of F-statistics. |
df2 |
Denominator degrees of freedom for p-value of F-statistics. |
fpvalue |
p-value for each F-statistics. |
Muhammad Imdad Ullah, Muhammad Aslam
Cule, E. and De lorio, M. (2012). A semi-Automatic method to guide the choice of ridge parameter in ridge regression. arXiv:1205.0686v1 [stat.AP].
Hoerl, A. E., Kennard, R. W., and Baldwin, K. F. (1975). Ridge Regression: Some Simulation. Communication in Statistics, 4, 105-123. doi: 10.1080/03610927508827232.
Hoerl, A. E. and Kennard, R. W., (1970). Ridge Regression: Biased Estimation of Nonorthogonal Problems. Technometrics, 12, 55-67. doi: 10.1080/00401706.1970.10488634.
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.
The ridge model fitting lmridge
mod <- lmridge(y~., as.data.frame(Hald), K = c(0, 0.0132, 0.1)) summary(mod) ## coefficients for first biasing parameter summary(mod)$summaries[[1]]$coefficients summary(mod)$summaries[[1]][[1]] ## ridge related statistics from summary function summary(mod)$summaries[[1]]$stats ## Ridge F-test's p-value summary(mod)$summaries[[1]]$fpvalue
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