\Average leverage"
Plots:
# of parameters = 1 = :03
sample size
247
A \large" leverage value would be
of parameters ! = 2(:03) = :06??
2 # sample
size
High leverage:
inuence(i) vs. ^i
inuence(i) vs. case number
These plots indicate whether large inuence values arise from \outliers" or
\cases with extreme covariate values".
Why not look at ri and 1;hihi
separately?
hi > :5
Moderate leverage: :2 < hi < :5
1136
1137
It may be quite informative to further
examine inuential cases:
Consider inuence of goodness of t
statistics:
1. \bad" data: miscoded covariate
value or miscoded response
1. Change in Pearson X 2 when the
i-th covariate pattern is deleted
(DIFCHISQ)
2. set aside \extreme" cases.
Xi2 = ri2=(1 ; hi)
(a) Fit a model to the \typical
cases".
(b) Discuss \extreme" cases separately
3. Discover unexpected phenomena
1138
2. Change in the deviance when the
i-th covariance pattern is deleted
(DIFDEV)
2
Di = d2i + (1r;i hhi )
i
=: d2i =(1 ; hi)
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0
PROC LOGISTIC provides measures
of inuence for individual parameters.
1
h
C bari = ri2 @ i A
1 ; hi
Xi2 = (C bari)( h1 )
1. Delete the i-th covariance pattern
i
An \extreme" set of covariate values
may have a strong \inuence" on only
one, or two, or a few values for parameter estimates.
1140
Use an approximation
^ = (X 0V^ X );1xi(Yi ; ni^i)=(1 ; hi)
(i)
=
2 3
66 ^. 0(i) 77
64
. 7
^ 5
k(i)
Then, for the j -th coecient,
^
DFBETAj;(i) = S j;(i)
^j
1142
2. Compute
^j;all data ; ^j;i;th cov. pattern deleted
S^
all data
j;
This requires too much computation.
1141