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

Independent correlation structure:
two models

Model 4. Uses empiricals^b;
fnot fixed

Model 5. Uses model-baseds^b;
ffixed at 1

BUT

b not affected

Sbaffected

Independent working correlation
matrix

COL1 COL2 ... COL9

ROW1 1.0000 0.0000 ... 0.0000
ROW2 0.0000 1.0000 ... 0.0000
ROW3 0.0000 0.0000 ... 0.0000
ROW4 0.0000 0.0000 ... 0.0000
ROW5 0.0000 0.0000 ... 0.0000
ROW6 0.0000 0.0000 ... 0.0000
ROW7 0.0000 0.0000 ... 0.0000
ROW8 0.0000 0.0000 ... 0.0000
ROW9 0.0000 0.0000 ... 1.0000

Measurements on same subject
assumed uncorrelated.

Model 4:Independent correlation
structure

Variable Coefficient

Empirical Std

Err

Wald

p-

value

INTERCEPT 1.4362 1.2272 0.2419
BIRTHWGT 0.0005 0.0003 0.1350
GENDER 0.0453 0.5526 0.9346
DIARRHEA 0.7764 0.5857 0.1849

Next, we examine output from models that

incorporate an independent correlation struc-

ture (Model 4andModel 5). The key difference

between Model 4 and a standard logistic

regression (Model 5) is that Model 4 uses the

empirical standard errors, whereas Model 5

uses the model-based standard errors. The

other difference is that the scale factor is not

preset equal to 1 in Model 4 as it is in Model 5.

These differences only affect the standard

errors of the regression coefficients rather

than the estimates of the coefficients them-

selves.

The working correlation matrix for an indepen-

dent correlation structure is the identity matrix

• with a 1 for the diagonal entries and a 0 for
  the other entries. The zeros indicate that the
  outcome measurements taken on the same
  subject are assumed uncorrelated.

The outputs for Model 4 and Model 5 (next

page) are shown on the left. The corresponding

coefficients for each model are identical as

expected. However, the estimated standard

errors of the coefficients and the

corresponding Wald test P-values differ for

the two models.

548 15. GEE Examples