Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

For example, even though, in the HWF model

being considered here, a test for EV 1 V 2 is

not dependent on the coding, a test forEV 1 or

EV 2 – which are lower order terms – may still

be dependent on the coding.

What this means is that in addition to requir-

ing that the model be HWF, we also require

that no tests be allowed for lower order com-

ponents of terms likeEV 1 V 2 already found to

be significant. We will return to this point later

when we describe the “hierarchy principle” for

retaining variables in the model.

We have now completed our recommendations

for variable specification as well as our require-

ment that the model be hierarchically well for-

mulated. When we complete this stage, we

have identified the largest possible model to

be considered. This model is the initial or start-

ing model from which we attempt to eliminate

unnecessary variables.

The recommended process by which the ini-

tial model is reduced to a final model is called

a hierarchical backward elimination (HWBE)

approach. This approach is described by the

flow diagram shown here.

In the flow diagram, we begin with the initial

model determined from the variable specifica-

tion stage.

If the initial model contains three-factor prod-

uct terms of the formEViVj, then we attempt to

eliminate these terms first.

Following the three-factor product terms, we

then eliminate unnecessary two-factor product

terms of the formEVi.

The last part of the strategy eliminates unnec-

essaryViandViVjterms.

EXAMPLE

HWF model:

logit PðXÞ¼aþbEþg 1 V 1 þg 2 V 2 þg 3 V 1 V 2

þd 1 EV 1 þd 2 EV 2 þd 3 EV 1 V 2

EV 1 V 2 :not dependenton coding

EV 1 orEV 2 :dependenton coding

Require

 HWF model
 No test for lower order
components of significant
higher order terms

VIII. The Hierarchical
Backward Elimination
Approach

üVariable specification
üHWF model

Largest model considered¼initial
(starting) model

Initial model

Initial model

Eliminate EViEj terms

Eliminate EVi terms

Eliminate Vi and ViVj terms

Final model

hierarchical

backward

elimination(HWBE)

184 6. Modeling Strategy Guidelines