parameters>#observations

)^binot valid
GEE approach: common set of
rs for each subject:

Subjecti:{r 12 ,r 13 ,r 14 ,r 23 ,r 24 ,

r 34 }

In general, forKsubjects:
rijk)rjk:#ofrs#by factor ofK

Example above:unstructuredcor-
relation structure

Next section shows other structures.

If there are more parameters to estimate than

observations in the dataset, then the model is

overparameterized and there is not enough

information to yield valid parameter estimates.

To avoid this problem, the GEE approach

requires that each subject have a common set of

correlation parameters. This reduces the number

of correlation parameters substantially. This

type of correlation matrix is presented at

the left.

There are now 6 correlation parameters (rjk)

for 12 observations of data. Giving each subject

a common set of correlation parameters

reduced the number by a factor of 3 (18 to 6).

In general, a common set of correlation para-

meters forKsubjects reduces the number of

correlation parameters by a factor ofK.

The correlation structure presented above is

called unstructured. Other correlation struc-

tures, with stronger underlying assumptions,

reduce the number of correlation parameters

even further. Various types of correlation

structure are presented in the next section.

EXAMPLE

3 subjects; 4 observations each

1 r 12 r 13 r 14 00000000

r 12 1 r 23 r 24 00000000

r 13 r 23 1 r 34 00000000

r 14 r 24 r 34 100000000

00001 r 12 r 13 r 14 0000

0000 r 12 1 r 23 r 24 0000

0000 r 13 r 23 1 r 34 0000

0000 r 14 r 24 r 34 10000

000000001 r 12 r 13 r 14

00000000 r 12 1 r 23 r 24

00000000 r 13 r 23 1 r 34

00000000 r 14 r 24 r 34 1

2

(^66)
(^66)
(^66)
(^66)
(^66)
(^66)
(^66)
(^66)
(^66)
4
3
(^77)
(^77)
(^77)
(^77)
(^77)
(^77)
(^77)
(^77)
(^77)
5
Now only 6rs for 12 observations:
##rs by factor of 3 (¼# subjects)
510 14. Logistic Regression for Correlated Data: GEE