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

EXAMPLE

MRSA example – Initial Model:

Logit PðXÞ¼aþb 1 E 1 þb 2 E 2 þg 1 V 1

þg 2 V 2 þd 11 E 1 W 1

þd 12 E 1 W 2 þd 21 E 2 W 1

þd 22 E 2 W 2 þd*E 1 E 2 ;

where

D¼MRSA statusð 0 ; 1 Þ;

E 1 ¼PREVHOSP

E 2 ¼PAMU;V 1 ¼W 1 ¼AGE;

V 2 ¼W 2 ¼GENDER

At least one collinearity problem,

i.e., involves PREVHOSP and

PREVHOSP × AGE Drop

Another possible collinearity problem

(CNI¼34.3)

Two alternatives at this point:

 Stop further collinearity

assessment

 Drop PAMUAGE and continue

We now illustrate the use of collinearity diag-

nostics for the MRSA dataset we have

described earlier. We consider the initial

model shown at the left, which contains two

Es, twoVs, 4EWs, and a singleEE.

Using the collinearity macro introduced above,

we obtain the (edited) collinearity diagnostic

output shown at the left. From this table, we

see that the highest CNI is 45.6, which is consid-

erably higher than 30, and there are two VDPs

greater than 0.5, corresponding to the variables

PREVHOSP (VDP¼0.95) and the product term

PREVHOSPAGE (VDP¼0.85).

Based on these results, we decide that there is

at least one collinearity problem associated

with the highest CNI and that this problem

involves the two variables PREVHOSP and

PREVHOSPAGE.

Proceeding sequentially, we would now drop

the product term from the model and reassess

collinearity for the resulting reduced model.

The results are shown at the left. From this

table, we see that the highest CNI is now 34.3,

which is slightly higher than 30, and there are

two VDPs greater than 0.5, corresponding to

the variables AGE (VDP¼0.74) and the prod-

uct term PAMUAGE (VDP¼0.75).

Since the highest CNI here (34.3) is only

slightly above 30, we might decide that this

value is not high enough to proceed further to

assess collinearity. Alternatively, proceeding

conservatively, we could drop the product

PAMUAGE and further assess collinearity.

274 8. Additional Modeling Strategy Issues