Hat Matrix Diagonal
Data points that are far from the centroid of
the Xspace are potentially influential.
A measure of the distance between a data point,
x_{i}, and the centroid of the
Xspace is the data point's associated diagonal
element h_{i} 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 h_{i} values
above this cutoff should be investigated.
For linear models, the hat matrix

H = X (X'X)^{1} X'
can be used as a projection matrix.
The hat matrix diagonal variable contains
the diagonal elements of the hat matrix

h_{i} = x_{i} (X'X)^{1} x_{i}'
For generalized linear models,
an approximate projection matrix is given by

H = W^{1/2}X (X'WX)^{1} X' W^{1/2}
where W = W_{o} when the full
Hessian is used and W = W_{e}
when Fisher's scoring method is used.
The values of h_{i} 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.