LMMstar (version 1.1.0)

CUSTOM: Custom Structure

Description

Variance-covariance structure specified by the user.

Usage

CUSTOM(
  formula,
  var.cluster,
  var.time,
  FCT.sigma,
  dFCT.sigma = NULL,
  d2FCT.sigma = NULL,
  init.sigma,
  FCT.rho,
  dFCT.rho = NULL,
  d2FCT.rho = NULL,
  init.rho,
  add.time
)

Value

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

Arguments

formula

formula indicating variables influencing the residual variance and correlation (right hand side).

var.cluster

[character] cluster variable.

var.time

[character] time variable.

FCT.sigma

[function] take as argument the model parameters, time, and design matrix. Output the vector of residuals standard deviations.

dFCT.sigma

[list of vectors] list whose elements are the first derivative of argument FCT.sigma.

d2FCT.sigma

[list of vectors] list whose elements are the second derivative of argument FCT.sigma (no cross-terms).

init.sigma

[numeric vector] initial value for the variance parameters.

FCT.rho

[function] take as argument the model parameters, time, and design matrix. Output the matrix of residuals correlation.

dFCT.rho

[list of matrices] list whose elements are the first derivative of argument FCT.rho.

d2FCT.rho

[list of matrices] list whose elements are the second derivative of argument FCT.rho (no cross-terms).

init.rho

[numeric vector] initial value for the correlation parameters.

add.time

not used.

Examples

## Compound symmetry structure
CUSTOM(~1,
       FCT.sigma = function(p,n.time,X){rep(p,n.time)},
       init.sigma = c("sigma"=1),
       dFCT.sigma = function(p,n.time,X){list(sigma = rep(1,n.time))},  
       d2FCT.sigma = function(p,n.time,X){list(sigma = rep(0,n.time))},  
       FCT.rho = function(p,n.time,X){
           matrix(p,n.time,n.time)+diag(1-p,n.time,n.time)
       },
       init.rho = c("rho"=0.5),
       dFCT.rho = function(p,n.time,X){
            list(rho = matrix(1,n.time,n.time)-diag(1,n.time,n.time))
       },
       d2FCT.rho = function(p,n.time,X){list(rho = matrix(0,n.time,n.time))}
)

## 2 block structure
rho.2block <- function(p,n.time,X){
   rho <- matrix(0, nrow = n.time, ncol = n.time)
   rho[1,2] <- rho[2,1] <- rho[4,5] <- rho[5,4] <- p["rho1"]
   rho[1,3] <- rho[3,1] <- rho[4,6] <- rho[6,4] <- p["rho2"]
   rho[2,3] <- rho[3,2] <- rho[5,6] <- rho[6,5] <- p["rho3"]
   rho[4:6,1:3] <- rho[1:3,4:6] <- p["rho4"]
   return(rho)
}
drho.2block <- function(p,n.time,X){
   drho <- list(rho1 = matrix(0, nrow = n.time, ncol = n.time),
                rho2 = matrix(0, nrow = n.time, ncol = n.time),
                rho3 = matrix(0, nrow = n.time, ncol = n.time),
                rho4 = matrix(0, nrow = n.time, ncol = n.time))   
   drho$rho1[1,2] <- drho$rho1[2,1] <- drho$rho1[4,5] <- drho$rho1[5,4] <- 1
   drho$rho2[1,3] <- drho$rho2[3,1] <- drho$rho2[4,6] <- drho$rho2[6,4] <- 1
   drho$rho3[2,3] <- drho$rho3[3,2] <- drho$rho3[5,6] <- drho$rho3[6,5] <- 1
   drho$rho4[4:6,1:3] <- drho$rho4[1:3,4:6] <- 1
   return(drho)
}
d2rho.2block <- function(p,n.time,X){
   d2rho <- list(rho1 = matrix(0, nrow = n.time, ncol = n.time),
                 rho2 = matrix(0, nrow = n.time, ncol = n.time),
                 rho3 = matrix(0, nrow = n.time, ncol = n.time),
                 rho4 = matrix(0, nrow = n.time, ncol = n.time))   
   return(d2rho)
}

CUSTOM(~variable,
       FCT.sigma = function(p,n.time,X){rep(p,n.time)},
       dFCT.sigma = function(p,n.time,X){list(sigma=rep(1,n.time))},
       d2FCT.sigma = function(p,n.time,X){list(sigma=rep(0,n.time))},
       init.sigma = c("sigma"=1),
       FCT.rho = rho.2block,
       dFCT.rho = drho.2block,
       d2FCT.rho = d2rho.2block,
       init.rho = c("rho1"=0.25,"rho2"=0.25,"rho3"=0.25,"rho4"=0.25))