#'
#' @title Computes the pooled parameters alpha and phi
#' @description This is an internal function required by the client
#' function \code{ds.gee}.
#' @param N a numeric vector, the sample sizes of the studies
#' @param npara the number of parameters/columns of the design matrix, for a regression
#' model, generated from the table of individual level data.
#' @param M_study
#' @param alphaM
#' @param sum_p
#' @param corStructure an integer that set the correlation structure: 1 for 'ar1',
#' 2 for 'exchangeable', 3 for 'independence', 4 for for 'fixed' and 5 for an
#' 'unstructure' correlation structure.
#' @keywords internal
#' @return a list which contains the individual elements of the input expression
#' @author Gaye, A.; Jones EM.
#'
geehelper1 <- function(N, npara, M_study, alphaM, sum_p, corStructure=NULL){
N <- sum(N)
npara <- npara[1]
phi<-(N-npara)^(-1)*sum(sum_p)
if(corStructure=="unstructured"){
M <- phi*((-999)-npara)
}else{
M <- phi*(sum(M_study)-npara)
}
if(length(alphaM) > 1){
dims <- c()
for(i in 1:length(alphaM)){
dims <- append(dims, length(alphaM[[i]]))
}
sum.alpha <- rep(0, max(dims))
for(i in 1:max(dims)){
for(s in 1:length(alphaM)){
sum.alpha[i] <- sum(sum.alpha[i],alphaM[[s]][i], na.rm=T)
}
}
}else{
sum.alpha <- unlist(alphaM)
}
alpha <- M^(-1)*sum.alpha
output <- list(alpha=alpha, phi=phi)
return(output)
}
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