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#'@title Build the joint covariance matrix
#'@name mc_build_C
#'@author Wagner Hugo Bonat
#'
#'@description This function builds the joint variance-covariance matrix
#' using the Generalized Kronecker product and its derivatives with
#' respect to rho, power and tau parameters.
#'
#'@param list_mu A list with values of the mean.
#'@param list_Ntrial A list with the number of trials. Useful only for
#' binomial responses.
#'@param rho Vector of correlation parameters.
#'@param list_tau A list with values for the tau parameters.
#'@param list_power A list with values for the power parameters.
#'@param list_Z A list of matrix to be used in the matrix linear
#' predictor.
#'@param list_sparse A list with Logical.
#'@param list_variance A list specifying the variance function to be
#' used for each response variable.
#'@param list_covariance A list specifying the covariance function to be
#' used for each response variable.
#'@param list_power_fixed A list of Logical specifying if the power
#' parameters are fixed or not.
#'@param compute_C Logical. Compute or not the C matrix.
#'@param compute_derivative_beta Logical. Compute or not the derivative
#' of C with respect to regression parameters.
#'@param compute_derivative_cov Logical. Compute or not the derivative
#' of C with respect the covariance parameters.
#'@keywords internal
#'@return A list with the inverse of the C matrix and the derivatives of
#' the C matrix with respect to rho, power and tau parameters.
mc_build_C <- function(list_mu, list_Ntrial, rho, list_tau, list_power,
list_Z, list_sparse, list_variance,
list_covariance, list_power_fixed,
compute_C = FALSE,
compute_derivative_beta = FALSE,
compute_derivative_cov = TRUE) {
n_resp <- length(list_mu)
n_obs <- length(list_mu[[1]][[1]])
n_rho <- n_resp * (n_resp - 1)/2
if (n_resp != 1) {
assert_that(n_rho == length(rho))
}
list_Sigma_within <- suppressWarnings(
Map(mc_build_sigma, mu = list_mu, Ntrial = list_Ntrial,
tau = list_tau, power = list_power, Z = list_Z,
sparse = list_sparse, variance = list_variance,
covariance = list_covariance,
power_fixed = list_power_fixed,
compute_derivative_beta = compute_derivative_beta))
list_Sigma_chol <- lapply(list_Sigma_within,
function(x) x$Sigma_chol)
list_Sigma_inv_chol <- lapply(list_Sigma_within,
function(x) x$Sigma_chol_inv)
Sigma_between <- mc_build_sigma_between(rho = rho, n_resp = n_resp)
II <- Diagonal(n_obs, 1)
nucleo <- kronecker(Sigma_between$Sigmab, II)
Bdiag_chol_Sigma_within <- bdiag(list_Sigma_chol)
t_Bdiag_chol_Sigma_within <- t(Bdiag_chol_Sigma_within)
Bdiag_inv_chol_Sigma <- bdiag(list_Sigma_inv_chol)
inv_C <- Bdiag_inv_chol_Sigma %*%
kronecker(solve(Sigma_between$Sigmab), II) %*%
t(Bdiag_inv_chol_Sigma)
output <- list(inv_C = inv_C)
if (compute_derivative_cov == TRUE) {
list_D_Sigma <- lapply(list_Sigma_within, function(x) x$D_Sigma)
## Derivatives of C with respect to power and tau parameters
list_D_chol_Sigma <-
Map(mc_derivative_cholesky, derivada = list_D_Sigma,
inv_chol_Sigma = list_Sigma_inv_chol,
chol_Sigma = list_Sigma_chol)
mat_zero <- mc_build_bdiag(n_resp = n_resp, n_obs = n_obs)
Bdiag_D_chol_Sigma <-
mapply(mc_transform_list_bdiag,
list_mat = list_D_chol_Sigma,
response_number = 1:n_resp,
MoreArgs = list(mat_zero = mat_zero))
Bdiag_D_chol_Sigma <- do.call(c, Bdiag_D_chol_Sigma)
D_C <- lapply(Bdiag_D_chol_Sigma, mc_sandwich_cholesky,
middle = nucleo,
bord2 = t_Bdiag_chol_Sigma_within)
## Finish the derivatives with respect to power and tau
## parameters
if (n_resp > 1) {
D_C_rho <-
mc_derivative_C_rho(D_Sigmab = Sigma_between$D_Sigmab,
Bdiag_chol_Sigma_within =
Bdiag_chol_Sigma_within,
t_Bdiag_chol_Sigma_within =
t_Bdiag_chol_Sigma_within,
II = II)
D_C <- c(D_C_rho, D_C)
}
output$D_C <- D_C
}
if (compute_C == TRUE) {
C <- t_Bdiag_chol_Sigma_within %*%
kronecker(Sigma_between$Sigmab, II) %*%
Bdiag_chol_Sigma_within
output$C <- C
}
if (compute_derivative_beta == TRUE) {
list_D_Sigma_beta <- lapply(list_Sigma_within,
function(x) x$D_Sigma_beta)
list_D_chol_Sigma_beta <-
Map(mc_derivative_cholesky, derivada = list_D_Sigma_beta,
inv_chol_Sigma = list_Sigma_inv_chol,
chol_Sigma = list_Sigma_chol)
mat_zero <- mc_build_bdiag(n_resp = n_resp, n_obs = n_obs)
Bdiag_D_chol_Sigma_beta <-
mapply(mc_transform_list_bdiag,
list_mat = list_D_chol_Sigma_beta,
response_number = 1:n_resp,
MoreArgs = list(mat_zero = mat_zero))
Bdiag_D_chol_Sigma_beta <- do.call(c, Bdiag_D_chol_Sigma_beta)
D_C_beta <- lapply(Bdiag_D_chol_Sigma_beta,
mc_sandwich_cholesky, middle = nucleo,
bord2 = t_Bdiag_chol_Sigma_within)
output$D_C_beta <- D_C_beta
}
return(output)
}
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