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

üSimplest choice forVs:

TheCs themselves (or a subset

ofCs)

SpecifyWs: (in model asEW):

RestrictWstobeVs themselves

or products of twoVs

(i.e., in model as E  V and

EViVj)

Most situations:

SpecifyVs andWsasCsor

subset ofCs

Rationale forWs (common sense):

Product terms more compli-

cated thanEViVjare as follows:

 Difficult to interpret

 Typically cause collinearity

üSimplest choice: useEViterms
only

The simplest choice for theVs is theCs them-

selves. If the number ofCs is very large, it may

even be appropriate to consider a smaller sub-

set of theCs considered to be most relevant and

interpretable based on prior knowledge.

Once theVs are chosen, the next step is to

determine theWs. These are the effect modi-

fiers that go into the model as product terms

withE, that is, these variables are of the form

EtimesW.

We recommend that the choice of Wsbe

restricted either to theVs themselves or to

product terms involving twoVs. Correspond-

ingly, the product terms in the model are

recommended to be of the formEtimesVand

EtimesVitimesVj, whereViandVjare two

distinctVs.

For most situations, we recommend that both

theVs and theWs be theCs themselves, or even

a subset of theCs.

As an example, if theCs are AGE, RACE, and

SEX, then a simple choice would have theVs

be AGE, RACE, and SEX and theWs be a sub-

set of AGE, RACE, and SEX thought to be

biologically meaningful as effect modifiers.

Therationalefor our recommendation about

theWs is based on the following commonsense

considerations:

 Product terms more complicated than

EViVjare usuallydifficult to interpreteven if

found significant; in fact, even terms of the

formEViVjare often uninterpretable.

 Product terms more complicated than

EViVjtypically will causecollinearity

problems; this is also likely forEViVjterms,

so the simplest way to reduce the potential

for multicollinearity is to useEViterms

only.

EXAMPLE

C 1 ,C 2 ,C 3 ,¼AGE, RACE, SEX

V 1 ,V 2 ,V 3 ,¼AGE, RACE, SEX

Ws¼subset of AGE, RACE, SEX

174 6. Modeling Strategy Guidelines