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

IV. Collinearity

Can someXs be predicted by other
Xs?

IfXs are “strongly” related, then

^bjunreliable

V^ar^bjhigh

model may not run

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collinearity

problem

Collinearity may involve more than

twoXs

+

Simple approach:rXi;Xjnotsufficient

EXAMPLE

IfX 3 X 1 X2,

could not detect this from

rX3,X 1 , rX3,X 2 ,orrX1,X 2.

Collinearityconcerns the extent to which one or

more of the predictor variables (theXs) in one’s

model can be predicted from otherXs in the

model.

If there are very strong relationships among

some of the Xs, then the fitted model may

yield unreliable regression coefficients for

some predictors. In other words, coefficients

may have high estimated variances, or perhaps

the model may not even run. When this occurs,

we say that the model has acollinearity problem.

Because collinearity problems may involve

relationships among more than twoXs, it is

not sufficient to diagnose collinearity by

simply looking at correlations among pairs of

variables.

For example, ifX3 was approximately equal to

the difference betweenX1 andX2, this relation-

ship could not be detected simply by looking at

correlations betweenX3 andX1,X3 andX2, or

X1 andX2.

EXAMPLE (continued)

Answer:

Scenarios ii and iv “legitimate”

screening

Scenarios i and iii incorrectly use

significance tests to screen

individualCi.

Scenario iii questionably uses BW

elimination onCs before assessing

interaction

Summary about Method 0:

1. Does not assess confounding or
   interaction for individualCi.


2. Makes most sense if model only
   involvesEs.

The answer to the above question is that sce-

narios ii and iv represent “legitimate” methods

of screening because both scenarios do not

involve using a significance test of a crude

effect betweenCiandD. Scenario iii differs

fromiin that backward elimination is (ques-

tionably) performed on theCs before interac-

tion is assessed.

Summarizing our main points about Method 0:

1. Method 0 does not consider confounding
   and/or interaction for predictors treated
   one-at-a-time.


2. Method 0 makes most sense when the
   model only involvesEs, but is questionable
   with bothEs andCs being considered.

270 8. Additional Modeling Strategy Issues