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

EXAMPLE (continued)

Results suggest that regression

coefficients are “influenced” by

these two subjects, e.g., drop

subjects 9 and/or 16 from data

+

Estimates ofa,b 1 ,b 2 ,g 1 ,g 2

meaningfully change

Possibly influential subjects other

than 9 and 16.

No Interaction Modelw/o subjects 9

and 16

Param DF Estimate Std Err exp[coeff]

Intercept 1 5.3830 0.8018 

PREVHOSP 1 1.6518 0.4237 5.217

PAMU 1 1.8762 0.3809 6.528

AGE 1 0.0370 0.0095 1.038

GENDER 1 0.9214 0.3809 2.513

No Interaction Modelfull data

Param DF Estimate Std Err exp[coeff]

Intercept 1 5.0583 0.7643 

PREVHOSP 1 1.4855 0.4032 4.417

PAMU 1 1.7819 0.3707 5.941

AGE 1 0.0353 0.0092 1.036

GENDER 1 0.9329 0.3418 2.542

Should influential subjects be
dropped from the data?

Answer: It depends!

 Incorrect data
 Incorrect model
 Legitimate and important data

These results indicate that if either or both of

these subjects are dropped from the dataset,

the collection of estimated regression coeffi-

cients in the fitted model would meaningfully

change, which, in turn, could result in mean-

ingfully different estimated ORs (e.g., exp½^b 1 Š).

Since the above figures consider only 42 of a

total of 289 subjects, there may be other influ-

ential subjects.

Without looking for other influential subjects,

we show on the left the output obtained for the

no-interaction model when subjects 9 and 16

are dropped from the dataset. Below this, we

provide the output for the same model for the

full dataset.

These results indicate that, particularly for the

E variables PREVHOSP and PAMU, corres-

ponding^bjand exp½^bjŠare somewhat different,

although both sets of results indicate strong

and statistically significant effects.

So, if we decide that some subjects (e.g., 9 and

16) are truly influential, what should we do?

Drop them from the dataset?

The answer, once again, is it depends! A large

influence statistic may be due to incorrect data

on one or more subjects, but it can also be the

result of an incorrect model, or even reflect the

legitimate importance of (correct) data on a

given subject.

278 8. Additional Modeling Strategy Issues