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

The reason why the model contains all fiveVs

at this point is because we have not yet done

any analysis to evaluate which of theVs can be

eliminated from the model.

However, because we have found two signifi-

cant interaction terms, we need to use the hier-

archy principle to identify certain Vs that

cannot be eliminated from any further models

considered.

The hierarchy principle says that all lower order

components of significant product terms must

remain in all further models.

In our example, the lower order components of

CATCHL are CAT and CHL, and the lower

order components of CATHPT are CAT and

HPT. Now the CAT variable is our exposure

variable, so we will leave CAT in all further

models regardless of the hierarchy principle.

In addition, we see that CHL and HPT must

remain in all further models considered.

This leaves theVvariables AGE, SMK, and

ECG as still being eligible for elimination at

the confounding stage of the strategy.

As we show in Chap. 7, we will not find sufficient

reason to remove any of the above three vari-

ables as nonconfounders. In particular, we will

show that decisions about confounding for this

example are too subjective to allow us to drop

any of the threeVterms eligible for elimination.

Thus, as a result of our modeling strategy, the

final model obtained contains the variables

CAT, AGE, CHL, SMK, ECG, and HPT as

main effect variables, and it contains the two

product terms CATCHL and CATHPT.

EXAMPLE (continued)

All fiveVs in model so far

Hierarchy principle

identifyVs thatcannotbe

eliminated

EVisignificant

+

EandVimust remain

CATCHL)CAT and CHL remain
CATHPT)CAT and HPT remain

Thus,

CAT (exposure) remains

plus

CHL and HPT remain

AGE, SMK, ECG

eligiblefor elimination

Results (details in Chap. 7):

Cannot remove AGE, SMK, ECG

(decisions too subjective)

Final model variables:

CAT, AGE, CHL, SMK, ECG, HPT,

CATCHL, and CATHPT

Presentation: X. An Example 191