Modeling and Multivariate Methods - SAS

196 Fitting Generalized Linear Models Chapter 6
Platform Commands
Table 6.3 Residual Formulas
Residual Type
Deviance
Studentized Deviance
Pearson
Studentized Pearson
Formula
r Di
= d i
( sign( y i
– μ i
))
r Di
=
sign( y i
– μ i
) d
-------------------------------------- i
φ( 1 – h i
)
r Pi
=
( y i
– μ i
)
-------------------
V( μ i
)
r Pi
=
y i
– μ
------------------------------------ i
V( μ i
)( 1 – h i
)
where (y i – μ i ) is the raw residual, sign(y i – μ i ) is 1 if (y i – μ i ) is positive and -1 if (y i – μ i ) is negative, d i is the
contribution to the total deviance from observation i, φ is the dispersion parameter, V(μ i ) is the variance
function, and h i is the i th diagonal element of the matrix W e (1/2) X(X'W e X) -1 X'W e (1/2) , where W e is the
weight matrix used in computing the expected information matrix. For additional information regarding
residuals and generalized linear models, see “The GENMOD Procedure” in the SAS/STAT User Guide
documentation.