Shrinkage After Estimation Using Heuristic Formulae
Description
Shrink regression coefficients using heuristic formulae, first described by Van Houwelingen and Le Cessie (Stat. Med., 1990)
Usage
1  shrink.heur(dataset, model, DF, int = TRUE, int.adj = FALSE)

Arguments
dataset 
a dataset for regression analysis. Data should be in the form
of a matrix, with the outcome variable as the final column. Application of the

model 
type of regression model. Either "linear" or "logistic". 
DF 
the number of degrees of freedom or number of predictors in the model. If DF is missing the value will be automatically estimated. This may be inaccurate for complex models with nonlinear terms. 
int 
logical. If TRUE the model will include a regression intercept. 
int.adj 
logical. If TRUE the regression intercept will be reestimated after shrinkage of the regression coefficients. If FALSE the regression intercept will be reestimated as described by Harrell 2001. 
Details
This function can be used to estimate shrunken regression coefficients based on
heuristic formulae (see References). A linear or logistic regression model with
an intercept is fitted to the data, and a shrinkage factor is estimated. The
shrinkage factor is then applied to the regression coefficients. If
int.adj == FALSE
the intercept value is estimated as described in
Harrell 2001.If int.adj == TRUE
the intercept value will be reestimated
by refitting the model with the shrunken coefficients.
The heuristic formula work by applying the number of model degrees of freedom (or the number of predictors) as a penalty, and so as the model becomes more complex, the necessary shrinkage increases, and the shrinkage factor becomes closer to zero.
Value
shrink.heur
returns a list containing the following:
raw.coeff 
the raw regression model coefficients, preshrinkage. 
shrunk.coeff 
the shrunken regression model coefficients 
lambda 
the heuristic shrinkage factor 
DF 
the number of degrees of freedom or number of predictors in the model 
Note
Warning: In poorly fitting models that includea large number of predictors the number of degrees of freedom may approch or exceed the model chi square. In such cases the shrinkage factor will be very small or even negative, and a different model building strategy is recommended.
References
Harrell, F. E. "Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis." Springer, (2001).
Harrell, F. E., Kerry L. Lee, and Daniel B. Mark. "Tutorial in biostatistics multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors." Statistics in medicine (1996) 15:361387.
Steyerberg, E. "Clinical Prediction Models" Springer (2009)
Van Houwelingen, J. C. and Le Cessie, S., "Predictive value of statistical models." Statistics in medicine (1990) 9:1303:1325.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  ## Example 1: Linear regression using the iris dataset
## shrinkage using a heuristic formula
data(iris)
iris.data < as.matrix(iris[, 1:4])
iris.data < cbind(1, iris.data)
set.seed(123)
shrink.heur(dataset = iris.data, model = "linear")
## Example 2: logistic regression using a subset of the mtcars data
## shrinkage using a heuristic formula
data(mtcars)
mtc.data < cbind(1,datashape(mtcars, y = 8, x = c(1,6,9)))
head(mtc.data)
set.seed(321)
shrink.heur(dataset = mtc.data, model = "logistic", DF = 3,
int = TRUE, int.adj = TRUE)

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