EXAMPLE (continued)Reduced model after diagnosing
collinearity:
Logit PðXÞ¼aþb 1 E 1 þb 2 E 2 þg 2 V 2
þd 12 E 1 W 2 þd 22 E 2 W 2
þd*E 1 E 2(Note:E 1 W 1 andE 2 W 1 removed from
initial model)V. Influential
Observations
Are there any subjects in the data-
set that “influence” study results?
- Does removal of subject from the
data result in “significant” change
in^bjorOR?^
Popular approach:
Measure extent of change in ^bj
when subject is dropped from the
data:
Delta-beta(Dbj)
The collinearity diagnostics resulting when
PAMUAGE is dropped from the model are
shown at the left. The largest CNI in this table
is 21.5, which is much smaller than 30. Thus,
we conclude that after we drop both PRE-
VHOSPAGE and PAMUAGE, there are no
more collinearity problems.So, after assessing collinearity in our MRSA
example, we have arrived at the reduced
model shown at the left. This model then
becomes a “revised” initial model from which
we determine a final (“best”) model using the
hierarchical backward elimination (HBWE)
strategy we have previously recommended.Another diagnostic issue concernsinfluential
observations:those subjects (if any) in one’s
dataset that strongly “influence” the study
results.Technically, a subject is an influential observa-
tion if removal from the dataset results in a
“significant” change in one or more of the esti-
mated bj (or ORs of interest in a logistic
model).A popular approach for identifying influential
observations is to compute for each study sub-
ject, a measure of the change in one or more
estimated regression coefficients when the
subject is dropped from the data. For a given
variable in the model, this measure is called a
Delta-beta.Presentation: V. Influential Observations 275