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.