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

Using the BWE approach, the least significant

EViVjterm, sayEV 1 V 3 , is eliminated from the

model first, provided it is nonsignificant, as

shown on the left-hand side of the flow. If it is

significant, as shown on the right-hand side of

the flow, then bothEV 1 V 3 and EV 1 V 2 must

remain in the model, as do all lower order

components, and the modeling process is

complete.

Suppose that theEV 1 V 3 term is not significant.

Then, this term is dropped from the model. A

reduced model containing the remaining

EV 1 V 2 term and all lower order components

from the initial model are then fitted. The

EV 1 V 2 term is then dropped if nonsignificant

but is retained if significant.

Suppose theEV 1 V 2 term is found significant,

so that as a result of backward elimination, it is

the only three-factor product term retained.

Then the above reduced model is our current

model, from which we now work to consider

eliminatingEVterms.

Because our reduced model contains the sig-

nificant termEV 1 V 2 , we must require (using

the hierarchy principle) that the lower order

componentsE,V 1 ,V 2 ,EV 1 ,EV 2 , andV 1 V 2 are

retained in all further models considered.

The next step is to assess the remainingEVi

terms. In this example, there is only oneEVi

term eligible to be removed, namely EV 3 ,

becauseEV 1 andEV 2 are retained from the

hierarchy principle.

EXAMPLE (continued)

BWE approach:

Suppose EV 1 V 3 least significant

and

nonsignificant

eliminate EV 1 V 3

from model

retain EV 1 V 3 and

EV 1 V 2 in model

and

significant

SupposeEV 1 V 3 not significant:
then dropEV 1 V 3 from model.
Reduced model:
EV 1 V 2
V 1 ,V 2 ,V 3 ,V 1 V 2 ,V 1 V 3
EV 1 ,EV 2 ,EV 3

EV 1 V 2 dropped if non-signif.

SupposeEV 1 V 2 significant:
thenEV 1 V 2 retained and above
reduced model is current model

Next: eliminateEVterms

From hierarchy principle:
E,V 1 ,V 2 ,EV 1 ,EV 2 , andV 1 V 2
retainedin all further models

Assess otherEViterms:
onlyEV 3 eligible for removal

Presentation: II. Interaction Assessment Stage 209