LMMstar (version 1.1.0)

TOEPLITZ: Toeplitz Structure

Description

Variance-covariance structure where the correlation depends on time elapsed between two repetitions. Can be stratified on a categorical variable.

Usage

TOEPLITZ(formula, var.cluster, var.time, type = "LAG", add.time)

Value

An object of class TOEPLITZ that can be passed to the argument structure of the lmm function.

Arguments

formula

formula indicating on which variable to stratify the residual variance and correlation (left hand side) and variables influencing the residual variance and correlation (right hand side).

var.cluster

[character] cluster variable.

var.time

[character] time variable.

type

[character] degree of flexibility of the correlation structure within covariate ("UN","LAG","CS"). Will also affect the variance structure when not explicit.

add.time

Should the default formula (i.e. when NULL) contain a time effect.

Details

formula: there can only be at most one covariate for the correlation structure. A typical formula would be ~1, indicating a variance constant over time and a correlation specific to each gap time.

type: for a binary covariate the correlation matrix can be decomposed into four blocs: A, B, B, C. A correspond the correlation within level 0 of the covariate, C within level 1, and B between level 0 and 1. Different correlation structures can be specified:

• "UN": unstructured matrix except for the diagonal elements of C which are constrained to be equal.

• "LAG": Toeplitz structure within A, B, and C, i.e. correlation specific to each time lag and covariate level.

• "CS": block-specific value except for C which has a different value for its diagonal elements.

Examples

## no covariate
TOEPLITZ(~time, var.cluster = "id", var.time = "time")
TOEPLITZ(gender~time, var.cluster = "id", var.time = "time")
TOEPLITZ(list(~time,~time), var.cluster = "id", var.time = "time")
TOEPLITZ(list(gender~time,gender~time), var.cluster = "id", var.time = "time")

## with covariates
TOEPLITZ(~side, var.cluster = "id", type = "UN",
         var.time = "time", add.time = TRUE)
TOEPLITZ(~side, var.cluster = "id", type = "LAG",
         var.time = "time", add.time = TRUE)
TOEPLITZ(~side, var.cluster = "id", type = "CS",
         var.time = "time", add.time = TRUE)
TOEPLITZ(gender~side, var.cluster = "id", type = "CS",
         var.time = "time", add.time = TRUE)