- Backward forCs, then
forward forECj:
Start withEand allCj,
j¼1,...,p
Sequentially drop
nonsignif.Cj
Sequentially addECjfor
remainingCj
COMMENTS/CRITICISMS OF
OPTIONS:
Option 2: next section.
Option 3:
þStarts with small-sized model
Can still be unreliable if large
number ofCs
Interactions not assessed
simultaneously
Option 4:
þFrequently used in practice (??)
Inappropriately uses statistical
testing to exclude potential
confounders
Questionably excludesCs before
assessingECs
Screening:
Good ways and questionable ways
Purpose:
Reduce number of predictors
Obtain a reliable and
interpretable final model
- Start with a model containing allCjterms,
proceed backward to eliminate nonsignificant
Cjterms, and then sequentially add statistically
significant product terms among the remain-
ingCjterms.
Option 2 above will be described in the next
section. It cannot be used, however, if initial
model does not run.Option 3 has the advantage of starting with a
small-sized model, but has two disadvantages:
the model may still have reliability problems if
there are a “large” number ofCs, and the for-
ward approach to assess interaction does not
allow all interaction terms to be assessed
simultaneously as with a backward approach.Option 4, which is frequently used in practice,
can bestrongly criticizedbecause it uses statis-
tical testing to determine whether potential
confounders Cj should stay in the model,
whereas statistical testing should not be used
to assess confounding. Furthermore, option 4
excludes potential confounders prior to asses-
sing interaction, whereas interaction should be
assessed before confounding.We now return to describe Option 1: screening.
As we will describe below, there are good ways
and questionable ways to carry out screening.The purpose of screening is to reduce the num-
ber of predictors being considered so that a
reliable and interpretable final model can be
obtained to help answer study questions of
interest.264 8. Additional Modeling Strategy Issues