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#' @title Test the Null hypothesis that all modalities are same
#' @description
#' Test null hypothesis that all modalities
#' have same observer performance ablity,
#' using Bayes factor.
#'
#' @details From input data (variable: \code{dataList}), the two objects
#' of class \strong{\emph{\code{stanfit}}}
#' are created. one is fitted to the null hypothesis model and
#' the another one representing
#' alternative hypothesis.
#' These two \strong{\emph{\code{stanfit}}}.
#' objects are compared by the Bayes factor.
#'
#' @inheritParams fit_Bayesian_FROC
#' @param dataList MRMC is the only case in which the function is available for this function.
#'
#' @return none
#' @export
#'
#@examples
# \dontrun{
#
# Test_Null_Hypothesis_that_all_modalities_are_same(BayesianFROC::dd)
#
# }#dontrun
Test_Null_Hypothesis_that_all_modalities_are_same <- function(
dataList,
ite =1111,
cha =1,
summary = FALSE
){
fitH0 <- fit_Bayesian_FROC( ite = ite, summary = summary, cha = cha, dataList = dataList , Null.Hypothesis = TRUE)
fitH1 <- fit_Bayesian_FROC( ite = ite, summary = summary, cha = cha, dataList = dataList , Null.Hypothesis = FALSE)
message("\n* Null model \n")
H0 <- bridgesampling::bridge_sampler(fitH0, method = "normal", silent = TRUE)
print(H0)
message("\n* Alternative model \n")
H1 <- bridgesampling::bridge_sampler(fitH1, method = "normal", silent = TRUE)
print(H1)
message("\n* Test the Null hypothesis that all modalities are same.\n")
BF10 <- bridgesampling::bf( H1,H0)
print(BF10)
message("\n* If the number is greater, then we reject H0 with more confidence.")
}#function
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