Hat Matrix Diagonal
Data points that are far from the centroid of
the X-space are potentially influential.
A measure of the distance between a data point,
xi, and the centroid of the
X-space is the data point's associated diagonal
element hi in the hat matrix.
Belsley, Kuh, and Welsch (1980) propose a cutoff
of 2 p/ n for the diagonal
elements of the hat matrix, where n is the
number of observations used to fit the model, and
p is the number of parameters in the model.
Observations with hi values
above this cutoff should be investigated.
For linear models, the hat matrix
can be used as a projection matrix.
The hat matrix diagonal variable contains
the diagonal elements of the hat matrix
H = X (X'X)-1 X'
hi = xi (X'X)-1 xi'
For generalized linear models,
an approximate projection matrix is given by
where W = Wo when the full
Hessian is used and W = We
when Fisher's scoring method is used.
H = W1/2X (X'WX)-1 X' W1/2
The values of hi are stored
in a variable named H_yname,
where yname is the response variable name.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.