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

We recommend (linear or logistic
models):

 Require CNI>> 30

 Focus on VDPs for largest CNI
 Address largest CNI before
other CNIs

Sequential approach

+

Drop variable, refit model, readdress

collinearity, continue until no collinearity

Option 1 – (most popular) Correct-
ing Collinearity:

EXAMPLE

Drop a variable from the model

Example:VDPs identifyX 1 ;X 2 ;X 1 X 2

+

DropX 1 X 2

Dropping a collinear variable:

 Does not mean variable is
nonsignificant

 Indicates dropped variable
cannot be assessed with other
collinear variables

Option 2 – Correction Collinearity:
Define a new (interpretable)
variable:

 Does not make sense for
product terms

 Can combine height and weight
into BMI¼height/weight^2

For either linear or logistic models, we recom-

mend that the largest CNI be “considerably”

larger than 30 before deciding that one’s

model is unreliable, and then focusing on

VDPs corresponding to the largest CNI before

addressing any other CNI.

This viewpoint is essentially a sequential

approach in that it recommends addressing

the most likely collinearity problem before con-

sidering any additional collinearity problems.

Once a collinearity problem has been deter-

mined, the most popular option for correcting

the problem is to drop one of the variables

identified (by the VDPs) to be a source of the

problem. If, for example, the VDPs identify two

main effects and their product, the typical solu-

tion is to drop the product term from the model.

Nevertheless, when such a term is dropped

from the model, this does not mean that this

term is nonsignificant, but rather that having

such a term with other variables in the model

makes the model unreliable. So, by dropping

an interaction term in such a case, we indicate

this interaction cannot be assessed, rather than

it is nonsignificant.

A second option for correcting collinearity is to

define a new variable from the variables caus-

ing the problem, provided this new variable is

(conceptually and/or clinically) interpretable.

Combining collinear variables will rarely make

sense if a product term is a source of the prob-

lem. However, if, for example, main effect vari-

ables such as height and weight were involved,

then the “derived” variable BMI (¼height/

weight^2 ) might be used to replace both height

and weight in the model.

Presentation: IV. Collinearity 273