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

The lower order components ofEV 2 V 5 are the

variablesE,V 2 ,V 5 ,EV 2 ,EV 5 ,andV 2 V 5 .Because

of the hierarchy principle, if the termEV 2 V 5 is

retained, then each of the above component

terms cannot be eliminated from all further

models considered in the backward elimination

process. Note the initial model has to contain

each of these terms, includingV 2 V 5 ,toensure

that the model is hierarchically well formulated.

In general, the hierarchy principle states that if

a product variable is retained in the model,

then all lower order components of that vari-

able must be retained in the model.

As another example, if the variablesEV 2 and

EV 4 are to be retained in the model, then the

following lower order components must also

be retained in all further models considered:

E,V 2 , and V 4. Thus, we are not allowed to

consider droppingV 2 andV 4 as possible non-

confounders because these variables must stay

in the model regardless.

Therationale for the hierarchy principleis simi-

lar to the rationale for requiring that the model

be HWF. That is, tests about lower order com-

ponents of variables retained in the model can

give different conclusions depending on the

coding of the variables tested. Such tests

should be independent of the coding to be

valid. Therefore, no such tests are appropriate

for lower order components.

For example, if the termEV 2 V 5 is significant,

then a test for the significance ofEV 2 may give

different results depending on whetherE is

coded as (0, 1) or (1, 1).

EXAMPLE

EV 2 andEV 4 retained:

Then

E, V 2 and V 4 also retained

cannot be considered as nonconfounders

Hierarchy Principle

If product variable retained, then
alllower order components must
be retained

Hiearchy principle rationale:

 Tests for lower order
components depend on coding
 Tests should be independent of
coding
 Therefore, no tests allowed for
lower order components

EXAMPLE

SupposeEV 2 V 5 significant: then the

test forEV 2 depends on coding ofE,

e.g., (0, 1) or (1, 1)

186 6. Modeling Strategy Guidelines