magic.post.proc             package: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)

Arguments:

       X: is the model matrix.

  object: is the list returned by 'magic' after fitting the  model with
          model matrix 'X'.

       w: is the weight vector used in fitting, or the weight matrix
          used  in fitting (i.e. supplied to 'magic', if one was.)
          't(w)%*%w' should typically give the inverse of the
          covariance matrix of the response data supplied to 'magic'.

Details:

     'object' contains 'rV' (V, say), and  'scale' (s, say) which can
     be  used to obtain the require quantities as follows. The Bayesian
     covariance matrix of  the parameters is VV's. The vector of 
     estimated degrees of freedom for each parameter is the leading
     diagonal of  VV'X'W'WX  where W is either the  weight matrix 'w'
     or the matrix 'diag(w)'. The  hat/influence  matrix is given by 
     WXVV'X'W' .

     The frequentist parameter estimator covariance matrix is 
     VV'X'W'WXVV's:  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

See Also:

     'magic'

