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

A summary of the printout for the model

remaining after interaction assessment is

shown here. In this model, the two interaction

terms are CH equals CATHPT and CC equals

CATCHL. The least significant of these two

terms is CH because the Wald statistic for this

term is given by the chi-square value of 9.86,

which is less significant than the chi-square

value of 23.20 for the CC term.

TheP-value for the CH term is 0.0017, so that

this term is significant at well below the 1%

level. Consequently, we cannot drop CH from

the model, so that all further models must con-

tain the two product terms CH and CC.

We are now ready to consider the confounding

assessment stage of the modeling strategy. The

first step in this stage is to identify all variables

remaining in the model after the interaction

stage. These are CAT, all fiveVvariables, and

the two product terms CATCHL and CAT

HPT.

The reason why the model contains all fiveVsat

this point is that we have only completed inter-

action assessment and have not yet begun to

address confounding to evaluate which of the

Vs can be eliminated from the model.

The next step is to apply the hierarchy principle

to determine which V variables cannot be

eliminated from further models considered.

The hierarchy principle requires all lower order

components of significant product terms to

remain in all further models.

The two significant product terms in our model

are CATCHL and CATHPT. The lower

order components of CATCHL are CAT and

CHL. The lower order components of CAT

HPT are CAT and HPT.

EXAMPLE (continued)

Printout:

Variable Coefficient S.E.

Chi
sq P
Intercept 4.0497 1.2550 10.41 0.0013
CAT 12.6894 3.1047 16.71 0.0000
AGE 0.0350 0.0161 4.69 0.0303
CHL 0.00545 0.0042 1.70 0.1923
Vs ECG 0.3671 0.3278 1.25 0.2627
SMK 0.7732 0.3273 5.58 0.0181

8

>>>>>

<

>>>>

>:

HPT 1.0466 0.3316 9.96 0.0016

CH 2.3318 0.7427 9.86 0.0017

CC 0.0692 0.3316 23.20 0.0000

CH = CAT × HPT and CC = CAT × CHL
remain in all further models

Ws

Confounding assessment:
Step 1. Variables in model:
CAT;AGE|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl};CHL;SMK;ECG;HPT
Vs
CAT|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}CHL;CATHPT;
EVs

All fiveVs still in model after
interaction

Hierarchy principle:

 DetermineVs that cannot be
eliminated
 All lower order components of
significant product terms remain

CATCHL significant)CAT and CHL

components

CATHPT significant)CAT and HPT

components

Presentation: V. The Evans County Example Continued 225