raiseR: Raise Regression and Robust Methods for Multicollinearity
Implements Raise Regression as an inference-preserving alternative to
Ridge Regression for combating multicollinearity in linear models, including
the classical single-variable Raise Regression, the Simultaneous Raise
Regression (SRR) based on QR decomposition and the Sequential Variance
Inflation Factor (SVIF) of Jacob and Varadharajan (2022)
<doi:10.1007/s11135-022-01557-9>, and the original raise parameter selection
strategy of Jacob and Varadharajan (2023) <doi:10.13189/ms.2023.110106>. Also
implements Robust Raise Regression for data contaminated by outliers, with
exact finite-sample inference (sandwich standard errors, Wald tests,
Satterthwaite-corrected degrees of freedom) obtained by down-weighting
observations using Stahel-Donoho projection outlyingness and Tukey's biweight
function. Provides ordinary and robust Ridge Regression (Hoerl and Kennard,
1970, <doi:10.1080/00401706.1970.10488634>), ordinary and robust Liu
Regression (Liu, 1993, <doi:10.1080/03610929308831027>), with the robust
variants of both based on the MM-estimates of Yohai (1987,
<doi:10.1214/aos/1176350366>) and, for Liu Regression specifically, the
biasing-parameter derivation of Filzmoser and Kurnaz (2018)
<doi:10.1080/03610918.2016.1271889>. Also provides the classical Variance
Inflation Factor (VIF) and Condition Number (Belsley, 1991) computed from
the correlation matrix of the predictors, and the Robust Variance Inflation
Factor (RVIF) and robust Condition Number of Jacob and Varadharajan (2024,
Sankhya B, <doi:10.1007/s13571-024-00342-y>), which use the same projection
outlyingness and biweight down-weighting scheme to obtain a weighted
correlation matrix that resists the influence of outliers. A flexible
scaleDat() function supports classical (mean and standard deviation), robust
weighted (Stahel-Donoho and Tukey biweight), median and Median Absolute
Deviation Normalized (MADN, the median absolute deviation scaled by 1.4826
to estimate the standard deviation under normality), and min-max scaling.
Diagnostic and goodness-of-fit plots, and the standard
influence-diagnostic suite (Cook's distance, DFBETAS and COVRATIO regression
diagnostics) and heteroskedasticity tests (via
the 'lmtest' and 'car' packages) analogous to those for objects of class
'lm', are provided for the exact, unbiased Raise Regression fit.
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