covariance_types {mmrm}

Covariance Types

Description

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.

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.

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.

See Also

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