AR1
Special case of autoregressive
Assumption:Yatt 1 andt 2 :
rt 1 ;t 2 ¼rjt^1 t^2 j
Cluster with four responses at
timet¼1, 2, 3, 4
1 rr^2 r^3
r 1 rr^2
r^2 r 1 r
r^3 r^2 r 12
6
6
4
3
7
7
5
Cluster with four responses at
timet¼1, 6, 7, 10
1 r^5 r^6 r^9
r^51 r^5 r^6
r^6 r^51 r^5
r^9 r^6 r^512
6
6
4
3
7
7
5
With AR1 structure, only oner
BUT
Order within clusternotarbitrary
AR1 is a special case of an autoregressive cor-
relation structure. AR1 is widely used because
it assumes only one correlation parameter and
because software packages readily accommo-
date it. The AR1 assumption is that the corre-
lation between any two responses from the
same subject equals a baseline correlation (r)
raised to a power equal to the absolute differ-
ence between the times of the responses.The correlation matrix to the left is for a
cluster that has four responses taken at time
t¼1, 2, 3, 4.Contrast this to another example of an AR1
correlation structure for a cluster that has
four responses taken at timet¼1, 6, 7, 10. In
each example, the power to which rho (r)is
raised is the difference between the times of
the two responses.As with the exchangeable correlation structure,
the AR1 structure has just one correlation
parameter. In contrast to the exchangeable
assumption, the order of responses within a
cluster is not arbitrary, as the time interval is
also taken into account.Presentation: VIII. Different Types of Correlation Structure 513