S-Type Ridge Regression

Implements S-type ridge regression, a robust and multicollinearity-aware linear regression estimator that combines S-type robust weighting (via the 'Stype.est' package) with ridge penalization; automatically selects the ridge parameter using the 'ridgregextra' approach targeting a close to 1 variance inflation factor (VIF), and returns comprehensive outputs (coefficients, fitted values, residuals, mean squared error (MSE), etc.) with an easy x/y interface and optional user-supplied weights. See Sazak and Mutlu (2021) , Karadag et al. (2023) < https://CRAN.R-project.org/package=ridgregextra> and Sazak et al. (2025) < https://CRAN.R-project.org/package=Stype.est>.

Styperidge.reg: An R package for the S-type ridge regression

This R package implements S-type ridge regression: a robust and multicollinearity-aware linear regression estimator that combines S-type robust weighting with ridge penalization. The method targets two common hurdles in linear modeling simultaneously: sensitivity to outliers and inflated variance due to severe multicollinearity. The S-type estimators were introduced by Sazak and Mutlu (2023) in “Comparison of the Robust Methods in the General Linear Regression Model.” The ridge parameter k is selected automatically via the approach implemented in the ridgregextra R package (Karadağ et al., 2023; Karadağ and Sazak, 2022), which targets variance inflation factor (VIF) values close to but not below 1 (following Kutner et al., 2004). For automatic ridge parameter selection, the package leverages the approach operationalized in the ridgregextra package, so users do not need to tune k manually. This package, in conjunction with the Stype.est package, offers a robust ridge regression solution adept at addressing issues of extreme multicollinearity and outliers, providing S-type ridge estimates without requiring manual adjustment of the ridge parameter. There are two functions in this package:

• Weightedridge.reg (sub-function): Given a data set and a user-supplied weight vector w, it returns the weighted ridge regression results (coefficients, fitted values, residuals, standard errors, and related diagnostics).

• regstyperidge (main function): Given x and y, it automatically determines the ridge parameter and returns the S-type ridge regression results end-to-end.

Features

• Robust ridge regression using S-type estimators (downweights outliers while stabilizing estimates under high collinearity).
• Automatic ridge parameter selection (no manual tuning required).
• Comprehensive outputs: coefficients, fitted values, residuals, model mean squared error (MSE), coefficient standard errors etc.
• Works with user-provided weights via Weightedridge.reg for advanced use cases.
• Simple main entry point (regstyperidge) with familiar x/y interface.

Installation

To install the package from GitHub, use the following command:

Installing Styperidge.reg development version

Please make sure that you installed devtools package first:

install.packages("devtools")

Install the package

devtools::install_github("filizkrgd/Styperidge.reg")

Installing Styperidge.reg from CRAN

install.packages( “Styperidge.reg”)

Installing Styperidge.reg development version

Example usage of the package.

When you install Styperidge.reg, required packages such as ridgregextra and Stype.est will be installed automatically via dependencies. For example data, you can install and load the isdals package (it contains the bodyfat data set).

• Prepare an example data set (bodyfat) from isdals:

library(isdals)
data(bodyfat)
x=bodyfat[,-1]
y=bodyfat[,1]

• Run regstyperidge function to get ridge regression results using the S-type ridge regression estimators.

regstyperidge=regstyperidge(x,y)
regstyperidge$MSE
regstyperidge$stdbeta

• Run Weightedridge.reg to fit weighted ridge regression with S-type estimators using x, y, and W (weights); returns coefficients, fitted values, residuals, standard errors, and diagnostics.

weightedridgereg=Weightedridge.reg(x,y,W)
weightedridgereg$MSE
weightedridgereg$stdbeta

References

• Karadağ, F. and Sazak, H.S., “R Algorithm for Ridge Parameter Estimation in Ridge Regression” Why R? Turkey 2022 Conference, online, Verbal, Summary Text, p.13, 2022. (https://www.nobelyayin.com/why-r-turkiye-2022-konferansi-18447.html)
• Karadağ, F., Sazak, H. S., and Aydın, O. (2023). ridgregextra: Ridge Regression Parameter Estimation. R package version 0.1.1. Available at CRAN. URL: https://CRAN.R-project.org/package=ridgregextra
• Kutner, M. H., Nachtsheim, C. J., Neter, J., and Li, W. (2004). Applied Linear Statistical Models
• Sazak, H. S., Karadağ, F., and Aydın, O. (2025). Stype.est: S-Type Estimators. R package version 0.1.0. URL: https://cran.r-project.org/web/packages/Stype.est/Stype.est.pdf
• Sazak, H. S., & Mutlu, N. (2021). Comparison of the robust methods in the general linear regression model. Communications in Statistics – Simulation and Computation, 52(7), 1–38. https://doi.org/10.1080/03610918.2021.1928196

Contact

For any questions please contact:

• Filiz Karadag, [email protected]
• Hakan Savas Sazak, [email protected]
• Olgun Aydin, [email protected]