SUMMARY (continued)
Issue 3: Collinearity
Diagnose using CNIs and VDPs
Collinearity detected if:
Largest CNI is large (>30)
At least 2 VDPs are large (0.5)
Difficulties:
How large is large for CNIs and
VDPs?
How to proceed if collinearity
problem?
Issue 4: Influential Observations
Does removal of subject from the
data result in “significant”
change in^bjorOR?d
Delta-beta(Dbj): measures chan-
ges in specificbjof interest
Cook’s distance-type (C):
combinesDbjover all predictors
(Xj)
Computer programs:
Provide plots of for each subject
Extreme plots indicate
influential subjects
Deleting influential observations:
Be careful!
Conservative approach: delete
only if data in error and cannot
be corrected
Issue 5: Multiple testing
The problem: should you adjusta
when performing
several tests?
For issue 3, we described how collinearity can
be diagnosed from two kinds of information,
condition indices(CNIs) and variance decom-
position proportions (VDPs). A collinearity
problem is indicated if the largest of the
CNIs is considered large (e.g.,>30) and at
least two of the VDPs are large (e.g.,0.5).Nevertheless, difficulties remaining when asses-
sing collinearity include how large is large for
CNIs and VDPs, and how to proceed (e.g.,
sequentially?) once a problem is identified.Issue 4, concerning influential observations,
is typically addressed using measures that
determine the extent to which estimated
regression coefficients are modified when
one or more data points (i.e., subjects) are
dropped from one’s model. Measures that
focus on such changes in specific regression
coefficients of interest are called Delta-betas,
whereas measures that combine changes over
all regression coefficients in one’s model are
called Cook’s distance-type measures.Computer programs for logistic regression
models provide graphs/figures that plot such
measures for each subject. Those subjects
that show extreme plots are typically identi-
fied as being “influential.”
The researcher must be careful when consid-
ering whether or not to delete an observation.
A conservative approach is to delete an obser-
vation only if it is obviously in error and can-
not be corrected.Issue 5 (multiple testing) concerns whether
or not the researcher should adjust the signif-
icance level used for significance tests to con-
sider the number of such tests that are
performed.284 8. Additional Modeling Strategy Issues