User Guide

119
Appendix
B
Covariance Structures
This appendix provides additional information on covariance structures.
Ante-Dependence: First-Order.
This covariance structure has
heterogenous variances and
heterogenous correlations
between adjacent elements. The
correlation between two non-
adjacent elements is the product
of the correlations between the
elements that lie between the
elements of interest.
AR(1). This is a first-order
autoregressive structure with
homogenous variances. The
correlation between any two
elements is equal to rho for
adjacent elements, rho
2
for
elements that are separated by a
third, and so on. Rho is
constrained so that –1< rho < 1.
AR(1): Heterogenous. This is a
first-order autoregressive
structure with heterogenous
variances. The correlation
between any two elements is
equal to rho for adjacent
elements, rho^2 for two elements
separated by a third, and so on.
Rho is constrained to lie between
–1 and 1.
s ssr ssrr ssrrr
ssr s ssr ssrr
ssrr ssr s ssr
ssrrr ssrr ssr s
1
2
2 11 3 112 4 1123
211 2
2
322 4223
3112 322 3
2
433
41123 4223 433 4
2
L
N
M
M
M
M
O
Q
P
P
P
P
s
rr r
rrr
rr r
rr r
2
23
2
2
32
1
1
1
1
L
N
M
M
M
M
O
Q
P
P
P
P
s ssr ssr ssr
ssr s ssr ssr
ssr ssr s ssr
ssr ssr ssr s
1
2
21 31
2
41
3
21 2
2
32 42
31 32 3
2
43
41 42 43 4
2
2
2
32
L
N
M
M
M
M
O
Q
P
P
P
P