SPSS® 12.0 Command Syntax Reference

Covariance Structure List
MIXED 993
The following is the list of covariance structures being offered by the MIXED procedure.
Unless otherwise implied or stated, the structures are not constrained to be non-negative definite
in order to avoid nonlinear constraints and to reduce the optimization complexity.
However, the variances are restricted to be non-negative.
• Separate covariance matrices are computed for each random effect; that is, while levels
of a given random effect are allowed to co-vary, they are considered independent of the
levels of other random effects.
AD1 First-order ante-dependence. The constraint
for stationarity.
≤ 1 is imposed
Example matrix:
2
σ1 σ 2 σ 1 ρ 1
AR1 First-order autoregressive. The constraint ρ ≤ 1 is imposed for stationarity.
Example matrix:
ARH1 Heterogenous first-order autoregressive. The constraint ρk ≤ 1 is imposed
for stationarity.
Example matrix:
ρ k
σ 2 σ 1 ρ 1 σ 3 σ 1 ρ 1 ρ 2 σ 4 σ 1 ρ 1 ρ 2 ρ 3
2
σ2 σ 3 σ 2 ρ 2
2
σ3σ1 ρ1ρ2 σ3σ2 ρ2 σ3 σ 4 σ 2 ρ 2 ρ 3
σ 4 σ 3 ρ 3
2
σ4σ1 ρ1ρ2 ρ σ
3 4σ2ρ 2ρ3 σ4σ3 ρ3 σ4 2
σ1 2
σ2σ ρ σ
1 2
1 ρ ρ 2 ρ 3
ρ 1 ρ ρ 2
ρ2 ρ 1 ρ
ρ3 ρ2 ρ 1
σ 2 σ 1 ρ σ 3 σ 1 ρ 2 σ 4 σ 1 ρ 3
σ3σ1 ρ 2 2
σ3σ2 ρ σ3 σ 3 σ 2 ρ σ 4 σ 2 ρ 2
σ 4 σ 3 ρ
σ4σ1 ρ 3 σ4σ2 ρ 2 2
σ4σ3 ρ σ4