rijk¼ri (^0) jkifi 6 ¼i^0
rA12 = rB12 = r 12
different clusters
Order {Yi 1 ,Yi 2 ,...,Yik}notarbi-
trary (e.g., cannot switchYA1and
YA4unless allYi 1 andYi 4 switched).
Fixed
User specifies fixed values forr.
r¼0.1 for first and fourth
responses; 0.3 otherwise
1 : 00 : 30 : 30 : 1
0 : 31 : 00 : 30 : 3
0 : 30 : 31 : 00 : 3
0 : 10 : 30 : 31 : 0
2
(^66)
4
3
(^77)
5
Norestimated.
Choice of structure not always
clear.
Like the other correlation structures, the same
set of correlation parameters are used for each
cluster. Thus, the correlation between the first
and second responses for cluster A is the same
as the correlation between the first and second
response for cluster B. This means that the
order of responses for a given cluster is not
arbitrary for an unstructured correlation struc-
ture. If we exchange the first and fourth
responses of clusteri, it does affect the analy-
sis, unless we also exchange the first and fourth
responses for all the clusters.
Fixed correlation structure.
Some software packages allow the user to
select fixed values for the correlation para-
meters. Consider the correlation matrix pre-
sented on the left. The correlation between
the first and fourth responses of each cluster
is fixed at 0.1; otherwise, the correlation is
fixed at 0.3.
For an analysis that uses a fixed correlation
structure, there are no correlation parameters
to estimate since the values of the parameters
are chosen before the analysis is performed.
Selection of a “working” correlation structure is
at the discretion of the researcher. Which struc-
ture best describes the relationship between
correlations is not always clear from the avail-
able evidence. For large samples, the estimates
of the standard errors of the parameters are
more affected by the choice of correlation
structure than the estimates of the parameters
themselves.
Presentation: VIII. Different Types of Correlation Structure 515