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

Fixed structure:rprespecified, not
estimated

In Model 3,rfixed at 0.55 for con-
secutive months; 0.30 for noncon-
secutive months.

Fixed working correlation matrix

COL1 COL2 ... COL9

ROW1 1.0000 0.5500 ... 0.3000
ROW2 0.5500 1.0000 ... 0.3000
ROW3 0.3000 0.5500 ... 0.3000
ROW4 0.3000 0.3000 ... 0.3000
ROW5 0.3000 0.3000 ... 0.3000
ROW6 0.3000 0.3000 ... 0.3000
ROW7 0.3000 0.3000 ... 0.3000
ROW8 0.3000 0.3000 ... 0.5500
ROW9 0.3000 0.3000 ... 1.0000

Correlation structure (fixed) for
Model 3: combines AR1 and
exchangeable features

Choice ofrat discretion of user,
but may not always converge

Allows flexibility specifying
complicatedCi

A fixed correlation structure has no correlation

parameters to estimate. Rather, the values of

the correlations are prespecified. For Model 3,

the prespecified correlations are set at 0.55

between responses from consecutive months

and 0.30 between responses from nonconsecu-

tive months. For instance, the correlation

between months 2 and 3 or months 2 and 1 is

assumed to be 0.55, whereas the correlation

between month 2 and the other months (not 1

or 3) is assumed to be 0.30.

This particular selection of fixed correlation

values contains some features of an autore-

gressive correlation structure, in that consecu-

tive monthly measures are more strongly

correlated. It also contains some features of

an exchangeable correlation structure, in that,

for nonconsecutive months, the order of mea-

surements does not affect the correlation. Our

choice of values for this model was influenced

by the fitted values observed in the working

correlation matrices of Model 1 and Model 2.

The choice of correlation values for a fixed

working correlation structure is at the discre-

tion of the user. However, the parameter esti-

mates are not guaranteed to converge for every

choice of correlation values. In other words,

the software package may not be able to pro-

vide parameter estimates for a GEE model for

some user-defined correlation structures.

The use of a fixed correlation structure con-

trasts with other correlation structures in that

the working correlation matrix (Ci) does not

result from fitting a model to the data, since

the correlation values are all prespecified. How-

ever, it does allow flexibility in the specification

of more complicated correlation patterns.

Presentation: II. Example 1: Infant Care Study 547