Obtains Bayesian parameter covariance matrix, frequentist
parameter estimator covariance matrix, estimated degrees of
freedom for each parameter and leading diagonal of influence/hat matrix,
for a penalized regression estimated by magic.
magic.post.proc(X,object,w=NULL)A list with three items:
the Bayesian covariance matrix of the model parameters.
the frequentist covariance matrix for the parameter estimators.
the leading diagonal of the hat (influence) matrix.
the array giving the estimated degrees of freedom associated with each parameter.
object contains rV (\( {\bf V}\), say), and
scale (\( \phi\), say) which can be
used to obtain the require quantities as follows. The Bayesian covariance matrix of
the parameters is \( {\bf VV}^\prime \phi\). The vector of
estimated degrees of freedom for each parameter is the leading diagonal of
\( {\bf VV}^\prime {\bf X}^\prime {\bf W}^\prime {\bf W}{\bf X}\)
where \(\bf{W}\) is either the
weight matrix w or the matrix diag(w). The
hat/influence matrix is given by
\( {\bf WX}{\bf VV}^\prime {\bf X}^\prime {\bf W}^\prime \)
.
The frequentist parameter estimator covariance matrix is \( {\bf VV}^\prime {\bf X}^\prime {\bf W}^\prime {\bf WXVV}^\prime \phi\): it is sometimes useful for testing terms for equality to zero.
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