shrink.lm

Internal function for <code>shrink</code>.

internal

The predictive value of a statistical model can often be improved
by applying shrinkage methods. This can be achieved, e.g., by regularized
regression or empirical Bayes approaches. Various types of shrinkage factors can
also be estimated after a maximum likelihood. While global shrinkage modifies
all regression coefficients by the same factor, parameterwise shrinkage factors
differ between regression coefficients. With variables which are either highly
correlated or associated with regard to contents, such as several columns of a
design matrix describing a nonlinear effect, parameterwise shrinkage factors are
not interpretable and a compromise between global and parameterwise shrinkage,
termed 'joint shrinkage', is a useful extension. A computational shortcut to
resampling-based shrinkage factor estimation based on DFBETA residuals can be
applied. Global, parameterwise and joint shrinkage for models fitted by lm(),
glm(), coxph(), or mfp() is available.

Daniela Dunkler

shrink

Global, Parameterwise and Joint Shrinkage Factor Estimation

Georg Heinze

shrink.lm function

<dl><dt>fit</dt>
<dd>a fit object of class <code>lm</code>, <code>glm</code>, <code>coxph</code>, or <code>mfp</code>.
The fit object must have been called with <code>x = TRUE</code> (and
<code>y = TRUE</code> in case of class <code>lm</code>).</dd>
<dt>type</dt>
<dd>of shrinkage, either <code>"parameterwise"</code> (default), <code>"global"</code>
shrinkage, or <code>"all"</code>.</dd>
<dt>method</dt>
<dd>of shrinkage estimation, either <code>"jackknife"</code> (based on
leave-one-out resampling, default) or <code>"dfbeta"</code> (excellent approximation
based on DFBETA residuals).</dd>
<dt>join</dt>
<dd>compute optional joint shrinkage factors for sets of specified columns
of the design matrix, if <code>type =</code> <code>"parameterwise"</code>. See details.</dd>
<dt>notes</dt>
<dd>print notes. Default is TRUE.</dd>
<dt>postfit</dt>
<dd>obtain fit with shrunken regression coefficients. This option
is only available for models without an intercept. Default is TRUE.</dd></dl>

Arguments

Global, Parameterwise and Joint Shrinkage of Regression Coefficients for Fit Object's of Class lm. — shrink.lm

<dl>

<dt>fit</dt>
<dd>a fit object of class <code>lm</code>, <code>glm</code>, <code>coxph</code>, or <code>mfp</code>.
The fit object must have been called with <code>x = TRUE</code> (and
<code>y = TRUE</code> in case of class <code>lm</code>).</dd>


<dt>type</dt>
<dd>of shrinkage, either <code>"parameterwise"</code> (default), <code>"global"</code>
shrinkage, or <code>"all"</code>.</dd>


<dt>method</dt>
<dd>of shrinkage estimation, either <code>"jackknife"</code> (based on
leave-one-out resampling, default) or <code>"dfbeta"</code> (excellent approximation
based on DFBETA residuals).</dd>


<dt>join</dt>
<dd>compute optional joint shrinkage factors for sets of specified columns
of the design matrix, if <code>type =</code> <code>"parameterwise"</code>. See details.</dd>


<dt>notes</dt>
<dd>print notes. Default is TRUE.</dd>


<dt>postfit</dt>
<dd>obtain fit with shrunken regression coefficients. This option
is only available for models without an intercept. Default is TRUE.</dd>

</dl>

ShrinkageFactors	cdot[rmInt]
ShrinkageFactorsVCOV	summary.glm(sfit)$cov.scaled
ShrunkenRegCoef	shcoef
postfit	pfit

shrink.lm: Global, Parameterwise and Joint Shrinkage of Regression Coefficients for Fit Object's of Class `lm`.

Description

Usage

Value

Arguments