Stationarym-dependent
Assumption:
Correlationskoccasions apart
same fork¼1, 2,...,m
Correlations>moccasions
apart¼ 0
Stationary 2-dependent, cluster
with six responses (m¼2,ni¼6)
1 r 1 r 2 000
r 1 1 r 1 r 2 00
r 2 r 1 1 r 1 r 2 0
0 r 2 r 1 1 r 1 r 2
00 r 2 r 1 1 r 1
000 r 2 r 1 12 6 6 6 6 6 6 4
3 7 7 7 7 7 7 5
Stationarym-dependent structure
)mdistinctrs
Unstructured
Cluster with four responses
#r¼4(3)/2¼ 6
1 r 12 r 13 r 14
r 12 1 r 23 r 24
r 13 r 23 1 r 34
r 14 r 24 r 34 12
6
6
4
3
7
7
5
nresponses
+
n(n1)/2 distinctrs,i.e.rjk 6 ¼rj (^0) k 0 unlessj¼j^0 andk¼k^0
r 126 ¼r 34 even ift 2 t 1 ¼t 4 t 3
Stationarym-dependent correlation
structure:
Theassumptionbehindtheuseof the stationary
m-dependent correlation structure is that cor-
relationskoccasions apart are the same for
k¼1, 2, ...,m, whereas correlations more
thanmoccasions apart are zero.
The correlation matrix to the left illustrates a
stationary 2-dependent correlation structure
for a cluster that has six responses. A station-
ary 2-dependent correlation structure has two
correlation parameters.
In general, a stationarym-dependent correla-
tion structure hasmdistinct correlation para-
meters. The assumption here is that responses
within a cluster are uncorrelated if they are
more thanmunits apart.
Unstructured correlation structure:
In an unstructured correlation structure there
are less constraints on the correlation para-
meters. The correlation matrix to the left is for
a cluster that has four responses and six corre-
lation parameters.
In general, for a cluster that hasnresponses,
there aren(n1)/2 correlation parameters. If
there are a large number of correlation para-
meters to estimate, the model may be unstable
and results unreliable.
An unstructured correlation structure has a
separate correlation parameter for each pair
of observations (j, k) within a cluster, even if
the time intervals between the responses are
the same. For example, the correlation
between the first and second responses of a
cluster is not assumed to be equal to the corre-
lation between the third and fourth responses.
514 14. Logistic Regression for Correlated Data: GEE