| magic.post.proc {mgcv} | R Documentation |
Auxilliary information from magic fit
Description
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.
Usage
magic.post.proc(X,object,w=NULL)
Arguments
X |
is the model matrix. |
object |
is the list returned by |
w |
is the weight vector used in fitting, or the weight matrix used
in fitting (i.e. supplied to |
Details
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.
Value
A list with three items:
Vb |
the Bayesian covariance matrix of the model parameters. |
Ve |
the frequentist covariance matrix for the parameter estimators. |
hat |
the leading diagonal of the hat (influence) matrix. |
edf |
the array giving the estimated degrees of freedom associated with each parameter. |
Author(s)
Simon N. Wood simon.wood@r-project.org