VIII. Different Types of
Correlation
Structure
Examples of correlation structures:
Independent
Exchangeable
AR1 autoregressive
Stationary m-dependent
Unstructured
Fixed
Independent
Assumption: responses uncorre-
lated within clusters
Matrix for a given cluster is the
identity matrix.
With five responses per cluster
10000
01000
00100
00010
000012 6 6 6 6 4
3 7 7 7 7 5
Exchangeable
Assumption: any two responses
within a cluster have same correla-
tion (r)
With five responses per cluster
1 rrrr
r 1 rrr
rr 1 rr
rrr 1 r
rrrr 12
6
6
(^66)
4
3
7
7
(^77)
5
We present a variety of correlation structures
that are commonly considered when per-
forming a correlated analysis. These correla-
tion structures are as follows: independent,
exchangeable, AR1 autoregressive, stationary
m-dependent, unstructured, and fixed. Soft-
ware packages that accommodate correlated
analyses typically allow the user to specify the
correlation structure before providing esti-
mates of the correlation parameters.
Independent correlation structure.
The assumption behind the use of the indepen-
dent correlation structure is that responses are
uncorrelated within a cluster. The correlation
matrix for a given cluster is just theidentity
matrix. The identity matrix has a value of 1
along the main diagonal and a 0 off the diago-
nal. The correlation matrix to the left is for a
cluster that has five responses.
Exchangeable correlation structure.
The assumption behind the use of the
exchangeable correlation structure is that any
two responses within a cluster have the same
correlation (r). The correlation matrix for a
given cluster has a value of 1 along the main
diagonal and a value ofroff the diagonal. The
correlation matrix to the left is for a cluster that
has five responses.
Presentation: VIII. Different Types of Correlation Structure 511