Covariance Structure List (MIXED command)
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.
AR1. First-order autoregressive.
ARH1. Heterogenous first-order autoregressive.
ARMA11. Autoregressive moving average (1,1).
CS. Compound symmetry. This structure has constant variance and constant covariance.
CSH. Heterogenous compound symmetry. This structure has non-constant variance and constant correlation.
CSR. Compound symmetry with correlation parameterization. This structure has constant variance and constant covariance.
DIAG. Diagonal. This is a diagonal structure with heterogenous variance. This is the default covariance structure for repeated effects.
FA1. First-order factor analytic with constant diagonal offset (d≥0).
FAH1. First-order factor analytic with heterogenous diagonal offsets (d k≥0).
HF. Huynh-Feldt.
ID. Identity. This is a scaled identity matrix.
TP. Toeplitz
TPH. Heterogenous Toeplitz
SP_POWER. Spatial power structure. Adapts the first-order autoregressive structure to
a time-decaying correlation of unequal-spaced and repeated measurements. This structure is only
supported on the REPEATED
subcommand.
SP_EXPONENTIAL. Spatial exponential structure. Assumes that time-decaying correlations
decrease exponentially with increasing spatial distances between repeated measurements. This
structure is only supported on the REPEATED
subcommand.
SP_GAUSSIAN. Spatial Gaussian structure. Assumes that time-decaying correlations
decrease more rapidly, with increasing spatial distances between repeated measurements, than for the
exponential structure. This structure is only supported on the REPEATED
subcommand.
SP_LINEAR. Spatial linear structure. Assumes that time-decaying correlations decrease
linearly with increasing spatial distances between repeated measurements. This structure is only
supported on the REPEATED
subcommand.
SP_LINEARLOG. Spatial linear-log structure. Assumes that time-decaying correlations
decrease linearly with increasing logarithmic spatial distances between repeated measurements. This
structure is only supported on the REPEATED
subcommand.
SP_SPHERICAL. Spatial spherical structure. Allows cubic terms of both the correlation
function and the spatial distances between repeated measurements. This structure is only supported
on the REPEATED
subcommand.
UN_AR1. UN@AR1. Specifies the Kronecker product of one unstructured matrix and the other first-order auto-regression covariance matrix. The first unstructured matrix models the multivariate observation, and the second first-order auto-regression covariance structure models the data covariance across time or another factor.
UN_CS. UN@CS. Specifies the Kronecker product of one unstructured matrix and the other compound-symmetry covariance matrix with constant variance and covariance. The first unstructured matrix models the multivariate observation, and the second compound symmetry covariance structure models the data covariance across time or another factor.
UN_UN. UN@UN. Specifies the Kronecker product of two unstructured matrices, with the first one modeling the multivariate observation, and second one modeling the data covariance across time or another factor.
UN. Unstructured. This is a completely general covariance matrix.
UNR. Unstructured correlations
VC. Variance
components. This is the default covariance structure for
random effects. When the variance components structure is specified
on a RANDOM
subcommand, a scaled
identity (ID
) structure is assigned
to each of the effects specified on the subcommand. If the variance
components structure is specified on the REPEATED
subcommand, it is replaced by the diagonal (DIAG
) structure.