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#-------------------------------------------------------------------------------
#' @title
#' Extracts the Standard Errors of the Coefficients for the 'Adapted Paik et Al.' Model
#'
#' @description
#' Extracts the standard errors for \eqn{\boldsymbol{\beta}} obtained with the
#' time-dependent frailty model proposed in the 'Adapted Paik et al.' framework.
#'
#' @param object An S3 object of class `AdPaik`, returned by the main model function
#' (`AdPaikModel`). This object contains all the optimal parameter estimates.
#'
#' @details
#' The `se.coef` function extracts the standard errors for the estimated parameters from the
#' `StandardErrorParameters` field in `object`.
#'
#' The function validates the structure of `object` and ensures compatibility
#' with the expected model output. It throws an error if the object is malformed or
#' inconsistent.
#'
#' @return A named list containing the categories of the standard errors for the optimal parameters.
#' @export
#'
#' @examples
#' # Example using the 'Academic Dropout' dataset
#' data(data_dropout)
#'
#' # Define the formula and time axis for the model
#' formula <- time_to_event ~ Gender + CFUP + cluster(group)
#' time_axis <- c(1.0, 1.4, 1.8, 2.3, 3.1, 3.8, 4.3, 5.0, 5.5, 5.8, 6.0)
#' eps <- 1e-10
#' categories_range_min <- c(-8, -2, eps, eps, eps)
#' categories_range_max <- c(-eps, 0, 1 - eps, 1, 10)
#'
#'\donttest{
#' # Run the main model
#' result <- AdPaikModel(formula, data_dropout, time_axis,
#' categories_range_min, categories_range_max, TRUE)
#'
#' # Extract the coefficients
#' coefseAdPaik(result)
#' }
coefseAdPaik <- function(object){
# Check object structure
check.result(object)
# Extract information from input variables
L <- n_intervals <- object$NIntervals
R <- n_regressors <- object$NRegressors
optimal_params <- object$StandardErrorParameters
beta = optimal_params[(L+1):(L+R)]
# Assign names to beta if regressors are provided
if (!is.null(object$Regressors) && length(object$Regressors) == R) {
names(beta) <- object$Regressors
}
return (beta)
}
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