{mgcv}R Documentation

Auxilliary information from magic fit


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.



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.


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 useful for testing terms for equality to zero.


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.


Simon N. Wood

See Also


[Package mgcv version 1.3-12 Index]