R/mc_derivative_sigma_beta.R

In mcglm: Multivariate Covariance Generalized Linear Models

#' @title Derivatives of V^{1/2} with respect to beta.
#' @author Wagner Hugo Bonat
#'
#' @description Compute the derivatives of \eqn{V^{1/2}} matrix with
#'     respect to the regression parameters beta.
#'
#' @param D A matrix.
#' @param D_V_sqrt_mu A matrix.
#' @param Omega A matrix.
#' @param V_sqrt A matrix.
#' @param variance A string specifying the variance function name.
#' @keywords internal
#' @return A list of matrices, containg the derivatives of \eqn{V^{1/2}}
#'     with respect to the regression parameters.

mc_derivative_sigma_beta <- function(D, D_V_sqrt_mu, Omega, V_sqrt,
                                     variance) {
    n_beta <- dim(D)[2]
    n_obs <- dim(D)[1]
    output <- list()
    if (variance == "power" | variance == "binomialP" |
            variance == "binomialPQ") {
        for (i in 1:n_beta) {
            D_V_sqrt_beta <- Diagonal(n_obs, D_V_sqrt_mu * D[, i])
            output[[i]] <-
                mc_sandwich_power(middle = Omega,
                                  bord1 = V_sqrt, bord2 = D_V_sqrt_beta)
        }
    }
    if (variance == "poisson_tweedie") {
        for (i in 1:n_beta) {
            D_V_sqrt_beta <- Diagonal(n_obs, D_V_sqrt_mu * D[, i])
            output[[i]] <- Diagonal(n_obs, D[, i]) +
                mc_sandwich_power(middle = Omega, bord1 = V_sqrt,
                                  bord2 = D_V_sqrt_beta)
        }
    }
    if (variance == "geom_tweedie") {
      for (i in 1:n_beta) {
        D_V_sqrt_beta <- Diagonal(n_obs, D_V_sqrt_mu * D[, i])
        output[[i]] <- Diagonal(n_obs, 2*D[, i]) +
          mc_sandwich_power(middle = Omega, bord1 = V_sqrt,
                            bord2 = D_V_sqrt_beta)
      }
    }
    return(output)
}