Estimation of a Shrinkage Factor for Linear Regression
Estimate a shrinkage factor for shrinkage-after-estimation techniques, with application to linear regression models.
ols.shrink(b, dat, sdm)
the shrinkage design matrix. This determines the regression coefficients that will be involved in the shrinkage process.
This is an accessory function that works together with
loocval to estimate a shrinkage factor. For further details,
see References. This function should not be used directly, and instead should
be called via one of the aforementioned shrinkage-after-estimation functions.
the function returns a shrinkage factor.
Currently, this function can only derive a single shrinkage factor for a given model, and is unable to estimate (weighted) predictor-specific shrinkage factors.
Harrell, F. E. "Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis." Springer, (2001).
Steyerberg, E. W. "Clinical Prediction Models", Springer (2009)
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## Shrinkage design matrix examples for a model with an ## intercept and 4 predictors: ## 1. Uniform shrinkage (default design within apricomp). sdm1 <- matrix(c(0, rep(1, 4)), nrow = 1) print(sdm1) ## 2. Non-uniform shrinkage; 1 shrinkage factor applied only to the ## first two predictors sdm2 <- matrix(c(0, 1, 1, 0, 0), nrow = 1) print(sdm2)