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[Stable]

Usage

cov_types(
  form = c("name", "abbr", "habbr"),
  filter = c("heterogeneous", "spatial")
)

Arguments

form

(character)
covariance structure type name form. One or more of "name", "abbr" (abbreviation), or "habbr" (heterogeneous abbreviation).

filter

(character)
covariance structure type filter. One or more of "heterogeneous" or "spatial".

Value

A character vector of accepted covariance structure type names and abbreviations.

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.

For all non-spatial covariance structures, the time variable must be coded as a factor.

Spatial Covariance structures:

StructureDescriptionParameters\((i, j)\) element
sp_expspatial exponential\(2\)\(\sigma^{2}\rho^{-d_{ij}}\)

where \(d_{ij}\) denotes the Euclidean distance between time points \(i\) and \(j\).

Abbreviations for Covariance Structures

Common Covariance Structures:

StructureDescriptionParameters\((i, j)\) element
adAnte-dependence\(m\)\(\sigma^{2}\prod_{k=i}^{j-1}\rho_{k}\)
adhHeterogeneous ante-dependence\(2m-1\)\(\sigma_{i}\sigma_{j}\prod_{k=i}^{j-1}\rho_{k}\)
ar1First-order auto-regressive\(2\)\(\sigma^{2}\rho^{\left \vert {i-j} \right \vert}\)
ar1hHeterogeneous first-order auto-regressive\(m+1\)\(\sigma_{i}\sigma_{j}\rho^{\left \vert {i-j} \right \vert}\)
csCompound symmetry\(2\)\(\sigma^{2}\left[ \rho I(i \neq j)+I(i=j) \right]\)
cshHeterogeneous compound symmetry\(m+1\)\(\sigma_{i}\sigma_{j}\left[ \rho I(i \neq j)+I(i=j) \right]\)
toepToeplitz\(m\)\(\sigma_{\left \vert {i-j} \right \vert +1}\)
toephHeterogeneous Toeplitz\(2m-1\)\(\sigma_{i}\sigma_{j}\rho_{\left \vert {i-j} \right \vert}\)
usUnstructured\(m(m+1)/2\)\(\sigma_{ij}\)

where \(i\) and \(j\) denote \(i\)-th and \(j\)-th time points, respectively, out of total \(m\) time points, \(1 \leq i, j \leq m\).

See also

Other covariance types: as.cov_struct(), cov_struct()