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

Note that if a model is HWF, then tests for the

highest-order terms in the model are always

independent of the coding of the variables in

the model. However, tests for lower order com-

ponents of higher order terms are still depen-

dent on coding.

For example, if the highest-order terms in an

HWF model are of the formEViVj, then tests for

all such terms are not dependent on the coding

of any of the variables in the model. However,

tests for terms of the formEViorViare depen-

dent on the coding and, therefore, should not

be carried out as long as the corresponding

higher order terms remain in the model.

If the highest-order terms of a HWF model are

of the formEVi, then tests forEViterms are

independent of coding, but tests forViterms

are dependent on coding of theVs and should

not be carried out. Note that because theVs

are potential confounders, tests forVs are not

allowed anyhow.

Note also, regarding the hierarchy principle,

that any lower order component of a significant

higher order term must remain in the model or

else the model will no longer be HWF. Thus, to

ensure that our model is HWF as we proceed

through our strategy, we cannot eliminate

lower order components unless we have elimi-

nated corresponding higher order terms.

EXAMPLE

HWF:EViVjhighest-order terms

Then tests for

EViVjindependentof codingbut

tests for

EViorVjdependenton coding

EXAMPLE

HWF:EVihighest-order terms

Then tests for

EViindependentof codingbuttests

for

Vidependenton coding

HWF model:

Tests forhighest-orderterms
independentof coding
but
tests forlower orderterms
dependenton coding

 Ensures that the model is HWF
e.g.,EViVjis significant
)retain lower order compo-
nents or else model is not
HWF

Presentation: IX. The Hierarchy Principle for Retaining Variables 187