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

CNIs and VDPs derived fromV^

CNIs identify if collinearity exists

VDPs identify variables causing
collinearity

SAS;STATA;SPSS

do not compute CNIs and VDPs

for nonlinear models

But:SAS macro available

Application of macro later

Difficulties:

How large is large for CNIs and
VDPs?
How to proceed if collinearity is
found?

Collinearity cut-off recommenda-
tions

ðBKW; 1981 Þ:CNI 30 ;VDP 0 : 5

+

Guidelines

for

linear regression models

Modifying guidelines for nonlinear
models:

 open question (lower CNI
cutpoint?)

 flexibility forhow high is high

The CNIs and VDPs previously introduced are

in turn derived from theV^ matrix. As illu-

strated earlier, the CNIs are used to identify

whether or not a collinearity problem exists,

and the VDPs are used to identify those vari-

ables that are the source of any collinearity

problem. (Again, see Kleinbaum et al., 2008,

Chapter 14, for a more mathematical descrip-

tion of CNIs, VDPs, andI^21 .)

Unfortunately, popular computer packages

such as SAS, STATA, and SPSS do not contain

programs (e.g., SASs LOGISTIC procedure)

that compute CNIs and VDPs for nonlinear

models. However, a SAS macro (Zack et al.),

developed at CDC and modified at Emory Uni-

versity’s School of Public Health, allows com-

putation of CNIs and VDPs for logistic and

other nonlinear models (see Bibliography).

We illustrate the use of this macro shortly.

Nevertheless, there are difficulties in diagnos-

ing collinearity. These include determining

how “large is large” for both the CNIs and the

VDPs, and how to proceed if a collinearity

problem is found.

The classic textbook on collinearity diagnostics

(Belsey, Kuh, and Welch, 1981) recommends a

cut-off of 30 for identifying a high CNI and a

cut-off of 0.5 for identifying a high VDP. Nev-

ertheless, these values were clearly described

as “guidelines” rather than firm cut-points, and

they were specified for linear models only.

To what extent the guidelines (particularly for

CNIs) should be modified (e.g., lowered) for

nonlinear models remains an open question.

Moreover, even for linear models, there is con-

siderable flexibility in deciding how high is high.

272 8. Additional Modeling Strategy Issues