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

However, we have restricted theVs to theCs

themselves primarily because there are a mod-

erately large number ofCs being considered,

and any further addition ofVsislikelyto

make the model difficult to interpret as well

as difficult to fit because of likely collinearity

problems.

We next choose theWs, which are the variables

that go into the initial model as product terms

withE(CAT). TheseWs are the potential effect

modifiers to be considered. TheWs that we

choose are theCs themselves, which are also

theVs. That is,W 1 throughW 5 equals AGE,

CHL, SMK, ECG, and HPT, respectively.

We could have considered other choices for the

Ws. For instance, we could have added two-

way products of the formW 6 equals AGE

CHL. However, if we added such a term, we

would have to add a corresponding two-way

product term as aVvariable, that is,V 6 equals

AGECHL, to make our model hierarchically

well formulated. This is because AGECHL is

a lower order component of CATAGE

CHL, which isEW 6.

We could also have considered for our set ofWs

some subset of the fiveCs, rather than all five

Cs. For instance, we might have chosen theWs

to be AGE and ECG, so that the corresponding

product terms in the model are CATAGE and

CATECG only.

Nevertheless, we have chosen theWs to be all

fiveCs so as to consider the possibility of inter-

action from any of the fiveCs, yet to keep the

model relatively small to minimize potential

collinearity problems.

Thus, at the end of the variable specification

stage, we have chosen as our initial model, the

E, V, Wmodel shown here. This model is writ-

ten in logit form as logit P(X) equals a constant

term plus terms involving the main effects of

the five control variables plus terms involving

the interaction of each control variable with

the exposure variable CAT.

EXAMPLE (continued)

Restriction ofVstoCs because:
 Large number ofCs
 AdditionalVs difficult to interpret
 AdditionalVs may lead to
collinearity

Choice ofWs:
(go into model asEW)
Ws¼Cs:
W 1 ¼AGE;W 2 ¼CHL;W 3 ¼SMK;
W 4 ¼ECG;W 5 ¼HPT

Other possibleWs:
W 6 ¼AGECHL

(IfW 6 is in model, then
V 6 ¼AGECHL also in HWF model.)

Alternative choice ofWs:
Subset ofCs, e.g.,

AGE)CATAGE in model

ECG)CATECG in model

Rationale forWs¼Cs:
 Allow possible interaction
 Minimize collinearity

InitialE,V,Wmodel

logit PðXÞ¼aþbCATþ~

5

i¼ 1

giVi

þCAT~

5

j¼ 1

djWj;

whereVis¼Cs¼Wjs

Presentation: X. An Example 189