# TOEPLITZ: Toeplitz Structure In LMMstar: Repeated Measurement Models for Discrete Times

 TOEPLITZ R Documentation

## 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)
``````

### 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.

### Value

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

### 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)
``````

LMMstar documentation built on Nov. 9, 2023, 1:06 a.m.