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

In the variable specification stage of our strat-

egy, we choose an initialE, V, Wmodel, shown

here, containing the exposure variable CAT,

fiveVs which are theCs themselves, and five

Ws which are also theCs themselves and which

go into the model as product terms with the

exposure CAT.

This initial model is HWF because the lower

order components of anyEViterm, namely,E

andVi, are contained in the model.

Note also that the highest-order terms in this

model are two-factor product terms of the form

EVi. Thus, we are not considering more com-

plicated three-factor product terms of the form

EViVjnorViterms that are of the formViVj.

The next step in our modeling strategy is to

consider eliminating unnecessary interaction

terms. To do this, we use a backward elimina-

tion (BWE) procedure to remove variables. For

interaction terms, we proceed by eliminating

(BWE) product terms one at a time.

The flow for our backward procedure begins

with the initial model and then identifies the

least significant product term. We then ask, “Is

this term significant?” If our answer isno,we

eliminate this term from the model. The model

is then refitted using the remaining terms. The

least significant of these remaining terms is

then considered for elimination.

This process continues until our answer to the

significance question in the flow diagram is

yes. If so, the least significant term is signifi-

cant in some refitted model. Then, no further

terms can be eliminated, and our process must

stop.

For our initial Evans County model, the BWE

allows us to eliminate the product terms of

CATAGE, CATSMK, and CATECG.

The remaining interaction terms are CAT 

CHL and CATHPT.

EXAMPLE (continued)

InitialE, V, Wmodel:

logit PðXÞ¼aþbCATþ~

5

i¼ 1

giVi

þE~

5

j¼ 1

djWj;

whereVs¼Cs¼Ws

HWF model because

EViin model

+

EandViin model

Highest order in model:EVi

noEViVjorViVjterms

Next step:

Interaction assessment using

backward elimination (BWE)

(Note: Chunk test for

H 0 :d 1 ¼d 2 ¼d 3 ¼d 4 ¼d 5 ¼ 0

is highly significant)

Backward elimination (BWE):

Initial model Find least significantproduct term

Do not drop terms

from model

Drop term

from model

Refit

model

significant?

STOP

Ye s N o

Interaction results:

Eliminated Remaining

CATAGE CATCHL

CATSMK CATHPT

CATECG

224 7. Modeling Strategy for Assessing Interaction and Confounding