covariance type
Format
vector of supported covariance structures. cov_type for common time points covariance structures,
cov_type_spatial for spatial covariance structures.
Details
abbreviation for covariance structures
Common Covariance Structures
| Structure | Description | Parameters | \((i, j)\) element |
| ad | Ante-dependence | \(m\) | \(\sigma^{2}\prod_{k=i}^{j-1}\rho_{k}\) |
| adh | Heterogeneous ante-dependence | \(2m-1\) | \(\sigma_{i}\sigma_{j}\prod_{k=i}^{j-1}\rho_{k}\) |
| ar1 | First-order auto-regressive | \(2\) | \(\sigma^{2}\rho^{\left \vert {i-j} \right \vert}\) |
| ar1h | Heterogeneous first-order auto-regressive | \(m+1\) | \(\sigma_{i}\sigma_{j}\rho^{\left \vert {i-j} \right \vert}\) |
| cs | Compound symmetry | \(2\) | \(\sigma^{2}\left[ \rho I(i \neq j)+I(i=j) \right]\) |
| csh | Heterogeneous compound symmetry | \(m+1\) | \(\sigma_{i}\sigma_{j}\left[ \rho I(i \neq j)+I(i=j) \right]\) |
| toep | Toeplitz | \(m\) | \(\sigma_{\left \vert {i-j} \right \vert +1}\) |
| toeph | Heterogeneous Toeplitz | \(2m-1\) | \(\sigma_{i}\sigma_{j}\rho_{\left \vert {i-j} \right \vert}\) |
| us | Unstructured | \(m(m+1)/2\) | \(\sigma_{ij}\) |
where \(i\) and \(j\) denote \(i\)-th and \(j\)-th time points, respectively, out of total \(m\) time points, \(1 \leq i, j \leq m\).
Note the ante-dependence covariance structure in this package refers to homogeneous ante-dependence, while the ante-dependence covariance structure from SAS PROC MIXED refers to heterogeneous ante-dependence and the homogeneous version is not available in SAS.