Covariance Types

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:

Structure	Description	Parameters	\((i, j)\) element
sp_exp	spatial 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:

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, \(1 \leq i, j \leq m\).