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

Chunk test

Not significant

Eliminate all

terms in chunk

or

Use BWE to eliminate terms

from chunk

Retain some

terms in chunk

Significant

Even if chunk test n.s.:

 Perform BWE

 May find highly signif. product
term(s)

 If so, retain such terms

For example, if there are a total of threeEViVj

terms in the initial model, namely, EV 1 V 2 ,

EV 1 V 3 , andEV 2 V 3 , then the null hypothesis

for this chunk test is that the coefficients of

these variables, sayd 1 ,d 2 , andd 3 are all equal

to zero. The test procedure is a likelihood ratio

(LR) test involving a chi-square statistic with

three degrees of freedom, which compares the

full model containing allVi,ViVj,EVi, andEViVj

terms with a reduced model containing onlyVi,

ViVj, andEViterms, with E in both models.

If the chunk testis not significant, then the

investigator may decide to eliminate from the

model all terms tested in the chunk, for exam-

ple, allEViVjterms. If the chunk testis signifi-

cant, then this means that some, but not

necessarily all terms in the chunk, are signifi-

cant and must be retained in the model.

To determine which terms are to be retained,

the investigator may carry out a backward

elimination (BWE) algorithm to eliminate

insignificant variables from the model one at

a time. Depending on the preferencen of the

investigator, such a BWE procedure may be

carried out without even doing the chunk test

or regardless of the results of the chunk test.

Alternatively, BWE may still be considered

even if the chunk test is nonsignificant. It is

possible that one or more product terms are

highly significant during BWE, and, if so,

should be retained.

As an example of such a backward algorithm,

suppose we again consider a hierarchically

well-formulated model that contains the two

EViVjtermsEV 1 V 2 andEV 1 V 3 in addition to

the lower order componentsV 1 ,V 2 ,V 3 ,V 1 V 2 ,

V 1 V 3 , andEV 1 ,EV 2 ,EV 3.

EXAMPLE

EV 1 V 2 ,EV 1 V 3 ,EV 2 V 3 in model

chunk test forH 0 :d 1 ¼d 2 ¼d 3 ¼ 0

use LR statisticw^23 comparing

full model: allVi,ViVj,EVj,EViVj,E

with reduced model:Vi,ViVj,EVj,E

EXAMPLE

HWF model:

EV 1 V 2 , EV 1 V 3 ,

V 1 ,V 2 ,V 3 ,V 1 V 2 ,V 1 V 3 ,

EV 1 ,EV 2 ,EV 3

208 7. Modeling Strategy for Assessing Interaction and Confounding