IV. Collinearity (pages 270–275)
A. The Problem:
If predictors (Xs) are “strongly” related, thenb^j
unreliable, V^ar^bjhigh, or model may not run.
B. Diagnosing Collinearity.
Use condition indices (CNIs) and variance
decomposition proportions (VDPs).
Collinearity detected if: largest CNI is large
(>30?)andat least 2 VDPs are large (0.5?)
C. Collinearity for Logistic Regression
Requires computer macro (program not
available in popular computer packages).
CNIs derived from inverse of Information Matrix
(I^21 )
D. Difficulties
How large is large for CNIs and VDPs? Guidelines
provided are “soft.”
How to proceed? We recommend sequential
procedure: fix one collinearity problem at a time.
How to fix problem? Usual approach: drop one of
the collinear variables; or, define new variable.
E. Example using MRSA data
V. Influential Observations (pages 275–279)
A. The Problem: Does removal of subject from the
data result in “significant” change in^bjordOR?
B. Measures: Delta-betas (Dbs) and Cook’s distance-
type measures (Cs).
C. Computer packages: provide plots ofDbs andCs
for each subject.
D. What to do with influential observations:
Not easy to decide whether or not to drop subject
from the data.
Conservative approach: drop subjects only if their
data is incorrect and cannot be corrected.
VI. Multiple Testing (pages 280–282)
A. The Problem: should you adjustawhen
performing several tests?
B. Bonferroni approach: Usea¼a 0 /T,where
a 0 ¼family-wise errorrate (FWER) and
T¼number of tests.
C. Criticisms of Bonferroni approach: low power;
based on unrealistic “universalH 0 ”; other.
D. Model building problem: number of tests (T)not
known in advance; therefore, no foolproof
approach.
VII. Summary (pages 283–285)288 8. Additional Modeling Strategy Issues