\Average leverage"
Plots:
# of parameters = 7 = :03
sample size 247
A \large" leverage value would be
of parameters! = 2(:03) = :06??
2 # sample
size
High leverage: hi > :5
Moderate leverage: :2 < hi < :5
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
separately?
1
hi
hi
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 when the
i-th covariate pattern is deleted
(DIFCHISQ)
Xi = ri =(1 hi)
2. set aside \extreme" cases.
(a) Fit a model to the \typical
cases".
(b) Discuss \extreme" cases separately
3. Discover unexpected phenomena
1138
2
2
2
2. Change in the deviance when the
i-th covariance pattern is deleted
(DIFDEV)
Di = di + (1ri hhi i)
=: di =(1 hi)
2
2
2
1139
C
bari =
Xi
2
0
2@
PROC LOGISTIC provides measures
of inuence for individual parameters.
1
hi A
hi
1
= (C bari)(h1i )
ri
1. Delete the i-th covariance pattern
2. Compute
^j;all data
An \extreme" set of covariate values
may have a strong \inuence" on only
one, or two, or a few values for parameter estimates.
all data
j;
This requires too much computation.
1141
1140
Use an approximation
= (X 0V^ X ) xi(Yi
2 ^ 3
66 i 77
= 64 ^. 75
k i
^
1
(i)
^ ) (1
ni i =
0( )
()
Then, for the j-th coeÆcient,
DFBETAj; i = S^j; i
()
()
^j
1142
^j;i th cov. pattern deleted
S^
hi
)